"In
the interest of clearness, it appeared to me inevitable that I should
repeat myself frequently, without paying the slightest attention to the
elegance of the presentation.
I adhered scrupulously to the
precept of that brilliant theoretical physicist,
L. Boltzmann, according to whom matters of
elegance ought to be left to the tailor and to the
cobbler." – A. E.

Recent
satellite and surface measurement systems are accurate enough to
determine the numerical values
of the flux elements of the global energy budget with such a precision
that allows us to draw quantitative assertions about the ratios and
internal relations of these components.

First we analyzed
two out/in type relationships:

-
planetary emissivity: the ratio
of the longwave radiation leaving the
atmosphere at the upper boundary to the longwave radiation entering
into the atmosphere
at the lower boundary;

- infrared
transparency: the ratio of longwave
radiation at the upper boundary which originates directly from the
surface to the surface upward longwave radiation.

We then recognized
the
following characteristics of the basic energy
fluxes:

— The energy balance equation
at the lower boundary (Earth's surface) shows a strong interrelation to
the energy balance at the upper boundary
(top-of-the-atmosphere);

— Most of the
observed radiative and non-radiative fluxes are integer multiples
of a unit flux, separately for the clear-sky, the cloudy, and the
global average (all-sky) fluxes;

We
offer some theoretical considerations (conceptual framework)
for these results in the Introduction. It begins
with some ideas based on the
literature; they are
then sublimated into questions, then into relationships to
be checked on
data,
forming a model, finally into equations and tables of data, leading to an almost-conclusive deduction of the flux
structure; this all is then sublimated into a justifiable forecast.

In the History
section we survey the evolution of our knowledge of the individual flux
components in the energy balance, based on the published global energy
budget diagrams.

"The
Earth’s climate is broadly regulated by three fundamental parameters:
the total solar irradiance, the planetary albedo and the planetary
emissivity. Observations from series of different satellites
during the last three decades indicate that these three quantities are
generally very stable. The total solar irradiation of some 1,361 W/m2
varies within 1 W/m2 during the 11-year solar cycle. The albedo is
close to 29 % with minute changes from year to year. The only exception
to the overall stability is a minor decrease in the planetary
emissivity (the ratio between the radiation to space and the radiation
from the surface of the Earth). This is a consequence of the increase
in atmospheric greenhouse gas amounts making the atmosphere gradually
more opaque to long-wave terrestrial radiation. As a consequence,
radiation processes are slightly out of balance as less heat is leaving
the Earth in the form of thermal radiation than the amount of heat from
the incoming solar radiation."

Lennart Bengtsson:
Foreword to the Special Issue on Observing and Modeling Earth's Energy
Flows
Surveys in Geophysics, 2012

PLANETARY EMISSIVITY

(the ratio between the radiation to space and the radiation from the
surface)

Our first question:
How opaque is our atmosphere to the terrestrial
radiation?

Second question: How
the surface energy balance looks
like? How much increase is expected
when the atmosphere is becoming more opaque?

Third question: How
the individual flux components in the surface and atmospheric
energy balance will change? How much increase of surface radiation,
sensible and latent heat, and downward atmospheric thermal
emission is awaited during global warming?

Trenberth and Fasullo (2012)
Fig. 1, with the original figure legend.374 W/m2 is
absorbed by the atmosphere and clouds out from 396 W/m2 upward longwave
surface radiation, and 22 W/m2
escapes to space through the atmospheric window.

The
value of the atmospheric window radiation was 40 W/m2 in the well-known
diagram of Kiehl and Trenberth (1997, hereafter KT97), repeated in the
third and fourth
assessment reports of the UN IPCC in 2001 and 2007. This value is a
result coming from two fundamental climate parameters: the
clear-sky
atmospheric window, and the cloud area fraction. The clear-sky longwave
transmittance cannot be measured, it must be computed. Though
satellites measure the outgoing longwave radiation also in the
mid-infrared window spectral region of 8 – 12 micrometer, the surface
radiation cannot be separated from the atmospheric radiation. So the
surface transmitted irradiance can only be computed by detailed
radiative transfer codes. The computational result of KT97 for the
surface radiation reaching the top-of-atmosphere in
the clear-sky
atmospheric window was 99 W/m2.

The
other parameter is the total single layer cloud area fraction (beta).
Clouds can be regarded opaque to the terrestrial longwave radiation,
except some very thin cloud layers or fog and haze (which are sometimes
partially accounted as clouds). KT97 mentioned 62 % total cloud cover,
but when computed their window radiation they calculated with 0.6 as (1
– 0.6) × 99 = 40 W/m2.
Recent radiative transfer computations
found that the 99 W/m2 of the clear-sky window radiation of KT97 was
too high; the proposed new value is significantly lower, 66 W/m2.
Therefore, the new all-sky window radiation would be (1 – 0.6)
×
66 = 26.4 W/m2. Using another, earlier data set for cloud area
fraction, where beta = 67% is given, the all-sky window radiation
is (1 – 0.67) × 66 = 22 W/m2. The authors of KT97 accepted
this
new computation, and displayed this value in their new diagram, see
above. Later we will argue that
the value of beta = 0.60 from the most recent satellite
observations should be used. We therefore regard the all-sky window
radiation to be about 26.5 W/m2, but a ±5 W/m2 uncertainty is allowed.

We
conclude here that for the longwave terrestrial radiation,
the Earth's atmosphere is partially transparent, but it is not too far
from being entirely opaque. About 94 % of the surface
longwave emission is absorbed in the atmosphere by the
greenhouse
gases, and only 6 % gets through and reaches the top-of-the-atmosphere
in the mid-infrared atmospheric window. Its opacity hence is 0.94 and
its transparency is 0.06. The surface transmitted irradiance in the
clear-sky atmosphere is STI(clear) = 66 W/m2, and, accepting an
effective single layer IR-opaque cloud area fraction beta = 0.6, the
all-sky surface transmitted irradiance is STI(all) = (1 –
beta) ×
STI(clear) = 26.4 ± 5 W/m2.

Answer
to the second question:

The surface energy balance equation
is:

Energy (SFC) = Energy absorbed = Energy released.

The
absorbed energy by the surface is the sum of shortwave and longwave
absorptions; the released energy is the sum of radiative and
non-radiative (turbulent) cooling.

The real case of the partially
transparent atmosphere of Earth can be approximated from the
perspective of a
100% 'closed-case'. A simple greenhouse model of
a planet closed into a 'glass-shell' is described in a basic
textbook: Figure 2.7 from John Marshall and Alan Plumb:
Atmosphere, Oceans and Climate Dynamics, Elsevier 2008, Chapter 2: The
global energy balance.

It is assumed that all the incoming
solar radiation gets through the atmosphere and reaches the surface
(that is, the 'shell' is completely transparent in the shortwave); and
all the longwave surface emission is absorbed by the
atmosphere
(that is, the shell is 100 % opaque in the longwave). It is also
assumed that no turbulent heat is transferred from the surface
to
the atmosphere: sensible and latent heating (SH and LH) is zero.

This
'glass shell atmosphere' is assumed to be entirely transparent to the
solar flux, that is, all the solar radiation reaches the surface and
being absorbed there; but this atmosphere absorbs the longwave upward
radiation from the ground completely. As a single-layer shell, it will
then radiate the absorbed energy upward and downward equally:

OLR
= DLR

The
constraint here is that in equilibrium the Absorbed Solar Radiation is
balanced by the Outgoing Longwave Radiation (OLR):

is
then equal to OLR in this model; therefore the normalized greenhouse
function, g = G/ULW is also equal to

g
= 0.5.

*

The
real Earth case is then looks like this.

It
is only partially transparent to the solar flux, so Shortwave
Absorbed by Atmosphere (SAA) is not zero, therefore Shortwave Absorbed
by Surface (SAS) is less than the total solar absorption: SAS = ASR –
SAA.

Also,
the real-Earth atmosphere is 'leaky', that is,only
partially opaque to the terrestrial flux, as shown in Figure 2.8 of
Marshall and Plumb (2008):

With the
data of Trenberth and Fasullo (2012):
the transmission in the cloudless atmosphere is STI(clear)/ULW = 66 /
396 = 1/6,
the fraction of terrestrial radiation which is absorbed by
the
atmosphere in the clear-sky case,
therefore the atmospheric opacity is ε
= 5/6.
In the
global average all-sky case ε = 14/15,
that is, the terrestrial LW emission beingtransmitted through the
atmosphere
(the atmospheric
transparency) is (1 – ε) = 1/15.

*

For
the surface energy balance equation of Earth, let us compute first the
clear-sky part of the atmosphere.

Citing
the data from the NASA CERES (Clouds and the Earth's Radiant Energy
System) satellite observations, as presented in the EBAF (Energy
Balanced And Filled) products, the latest editions Ed2.7 and Ed2.8 on
theNASA
CERES website give for the ten-year period 2000 - 2010:

This equality alone is enough to
question the accepted theory of CO2-induced
surface warming as it expresses that, according to the observed and
published NASA data, the clear-sky surface energy budget of the Earth
is unequivovally predetermined by the outgoing radiation at the top of
the atmosphere.

To compare it with 2OLR(all), the difference is +28.2 W/m2, and to
compare it with 2OLR(clear), the difference is -24.2 W/m2.

These
values are similar to the energy being lost in the all-sky atmospheric
window.

So it can be written, numerically, within the observation error, that

E(SFC, all) =
2OLR(clear) – STI(all).

This
relationship would mean that the
Earth's all-sky atmosphere works like an LW-opaque closed shell,
except one-fifteenth of the surface irradiance which is
escaping to space through the all-sky atmospheric window.

***

Here
another quantity will be taken into account: the difference of
clear-sky and all-sky outgoing radiations, OLR(clear) –
OLR(all),
called the Long Wave Cloud Radiative Effect, LWCRE; known
also as the 'blanketing effect' of the clouds(in
contrast to their shielding effect in the SW). It is equivalent to G(all) –
G(clear), therefore LWCRE also gives the Greenhouse Effetc of
Clouds.

According to the CERES EBAF data:

OLR(clear) – OLR(all) = G(all) – G(clear) = LWCRE = 26.5 ± 0.5 W/m2.

Let
us compare it to the atmospheric window value: it was STI(all) = 26.4
W/m2.

The
longwave radiative effect of clouds, LWCRE, seems to be the same as the
all-sky atmospheric window, STI(all); it seems that the role of the
partial cloud cover in the longwave is to close the atmospheric window.This
would explain the similar behavior of a closed shell model and the open
atmospheric model of the partially cloud-covered Earth.

We
show the concept in our two
figures below:

Figure 1. Schematic view
representing the concept of a 'leaky' atmosphere.
Surface transmitted irradiance, STI(all) is lost in space
through the open mid-infrared atmospheric window.

There
is solar absorption in the atmosphere:SAA
≠ 0, therefore SAS ≠ ASR;

and
the turbulent heat does not zero:SH
+ LH ≠ 0.

Further,
in the clear-sky Earth, the absorbed solar radiation is not equal to
the outgoing radiation: ASR(clear)
≠ OLR(clear).

Contrary to all of these internal
differences, the
above-shown logic still seems to work.

Answer to the
third question:

There is a pattern in Earth's energy balance: the
individual flux components are integer
multiples of LWCRE, if using its more recent 26.6 W/m2 value (data
sources will be given later in this website in detail):

It
seems that these fluxes can change only if LWCRE is changing; but
LWCRE seems to be constrained to OLR(all)/9; and, in turn,
OLR(all) is
constrained to the absorbed solar radiation, ASR, within a small
imbalance.

Planetary
emissivity, ep
, defined as OLR(all)/ULW, called also the
all-sky transfer functionf(all), has a value
of 9/15= 0.6,
according to the table.
It is formally equal to (1 –g(all)), whereg(all) is the
normalized all-sky greenhouse function:

g(all)
= G(all)/ULW = (ULW – OLR(all)) / ULW =6/15= 0.4.

Let
us recall: both the planetary emissivity ep(transfer
function, f(all)),
and the greenhouse function of the closed-shell geometry were 0.5.

On
Earth, where 1/10 of the clear-sky emission is coming from the surface
and lost-in-space through
the open all-sky atmospheric window, we must have

f(all)
= 5/10 + 1/10 = 0.6g(all)
= 5/10 – 1/10 = 0.4

***

Another interesting relation: if the atmospheric clear-sky atmospheric
transparency is 1 – ε(clear) =1/6
and the all-sky transparency is (1 – ε(all)) =
1/15, then, knowing that the cloud cover is opaque in the infrared,
from the (1 – β) × 1/6 = 1/15 equation we have for the β cloud area
fraction a value of β = 3/5 = 0.6.Checking the observed total cloud area
fraction in the NASA CERES SYN1deg (2016) satellite product, we can see
that β ≈ 0.605.

This further means that, from the all-sky planetary emissivity of 9/15
we have its clear-sky value as
f(clear) = 9/15 + 1/15 = 10/15 = 2/3,

The
sharp values of these quantities are extremely unlikely, unless some
planetary-level determinations work in the physical background — or in
the geometry. We should regard these values as descriptions of an
annual global mean 'preferred' state, around which
oscillations
(vibrations, fluctuations,natural
or triggered variations)
are possible — unknown in size and time-scale.

***

We
show finally that the surface energy balance equation, which
connects unequivocally the energy budget of the lower boundary
(surface) to the energy flows at the upper boundary (TOA), can be
justified on the latest published energy budget diagram (Stephens and
L'Ecuyer 2015).

Though
an important energy flow component, clear-sky outgoing radiation,
OLR(clear) is not displayed here, we recall the earlier published
energy balance diagram by the same authors (Stephens et al. 2012: An
update on Earth's energy balance in light of the latest observations,
Nature Geoscience 5: 691-696), where the quantity is presented
as:

OLR(clear) (Clear-sky emission) = 266.4 ± 3.3 W/m2

Another fundamentalcomponents
presented in the Stephens et al. (2012) diagram is cloud longwave
effect at the surface:

with an imbalance of only 0.4 W/m2, being also indicated in the diagram(under
the name Net Absorbed).

The
relationship in this diagram is exact.

We can therefore establish E(SFC) as element 19=2×9+1 in
our table.

According
to these data,
the energy flows at the lower boundary of
the atmosphere (surface)
equilibrate to the energy flows
at the upper boundary (TOA).

The surface energy budget of the
Earth, both in the clear-sky and the all-sky case,
is unequivovally predetermined by the longwave radiations at the top of
the atmosphere.

If this relationship is valid and long-standing, no global warming in
the current sense
(gradual decrease in planetary emissivity and atmospheric transparency
as a consequence of the
atmospheric greenhouse gas amounts) could happen.

We cannot see any other reasonable physical understanding of this
equality than this one: the opacity
of the Earth's atmosphere to long-wave terrestrial radiation is
entirely determined by the specific
'leaky-but-still-closed' shell geometry, controlled
by the top-of-atmosphere (TOA) energetic constraints and regulated by
the ratios and relationships of the fluxes.
These annual global mean fluxes, including
downward longwave
radiation, latent heat release and the greenhouse effect itself, could
change only with the absorbed solar energy.

With
these energy budget relationships and integer flux patterns (which
reveal themselves within the published data), augmented by our proposed
theoretical framework (approximating the real-Earth
case from the opaque limit), we think the ruling paradigm is seriously
challenged.

Technical foreword

The most important
components of the Earth’s global
energy budget are: Incoming Solar Radiation (ISR); Reflected Solar
Radiation
(RSR); their ratio: α = RSR/ISR the planetary albedo; Absorbed Solar
Radiation,
ASR = ISR – RSR. And further: Outgoing Longwave Radiation (OLR), which
in a
longer period of time equilibrates to Absorbed Solar Radiation: OLR =
ASR. Then
Downward Longwave Radiation (DLR), emitted from the atmosphere downward
and measured
at the surface, called also Back Radiation; and Upward Long Wave (ULW)
radiation, emitted by the surface (Planck-, or black-body, or thermal,
or
infrared radiation).

The Absorbed Solar
Radiation is partitioned into two portions:
one is absorbed by the atmosphere and clouds (Solar Absorbed by
Atmosphere,
SAA), and the remaining portion which is absorbed by the surface (Solar
Absorbed by Surface, SAS; evidently SAA + SAS = ASR).

We
have also two
non-electromagnetic (non-radiative) fluxes from the surface into the
atmosphere: Sensible Heating (SH) and Latent Heating (LH), the latter
termed also
Evaporation (E). Sensible heat is mainly convection, that is, a
material current of ascending warm air masses, called also 'thermals',
and only a
little part of it is heat-conduction. Latent heat release
happens
by phase change of water vapor into condensed matter; its value, on the
global scale, can be evaluated from water cycle analyses. These
processes are 'cooling' if looking from a surface
perspective. For short, the sum (SH + LH) is often referred to as
the 'turbulent' flux.

We may insert also
the flux components of solar radiation
that reaches the surface, Downward Solar Radiation (DSR), and Upward
Short Wave
(USW) which is reflected from Earth’s land-ocean surface, where the
solar absorbed by surface is their difference: SAS =
DSR – USW,
connected to a surface albedo.

And there is a cloud
area fraction, β.

So
we have seven
observed flux parameters: three longwave,
ULW, OLR and DLR; two shortwave, SAA and SAS, and the turbulent energy
flows:
SH and LH; and we have two energy balance equations between them: the
long-term equilibrium relationship between the absorbed solar and the
outgoing longwave radiation at
the top of the atmosphere (TOA):

E(TOA) = ASR = OLR

and the equality of
the absorbed
(shortwave plus longwave) and the released (radiative plus
non-radiative)
energy flows at the surface (SFC):

These are the
so-called all-sky fluxes, which are observed
under global average meteorological conditions in the cloudless and
cloudy part
of the atmosphere. The ‘fair weather fluxes’ are given separately as
clear-sky
fluxes. We indicate them as, for example, OLR(all) and OLR(clear), or
DLR(all)
and DLR(clear). ULW is the only one which is regarded the same in the
global annual
mean. The cloudy fluxes can be given similarly, for example the annual
global mean
solar absorbed by surface under clouds is SAS(cloudy).

Several composite
fluxes can be created as linear
combinations of the primary fluxes. We mention here first the
difference of
clear-sky and all-sky outgoing longwave radiations, OLR(clear) –
OLR(all),
which is the Cloud Long Wave Radiative Effect, LWCRE:

OLR(clear) –
OLR(all) = LWCRE.

It will play an
important
role in the followings.

*

These fluxes are
typically described by two parameters: a
measured (observed) value, F, and an uncertainty of that observation,
given as
one standard deviation, ± 1σ.

In our study we are
going to assign a third parameter to most
of them, which we call the F0 value, and will be
generated
as F0 = I × UNIT. Here I is an integer, and UNIT
is a unit flux. In
the all-sky case, I is between 1 and 15, and the unit flux is LWCRE, as
measured by NASA CERES, and presented in, for example, the updated
global
energy balance diagram of Stephens et al. (2012) as LWCRE = 26.6 ± 5
W/m2.

Our F0(all)
values will be one of the following:

26.6

2 x 26.6 = 53.2

3 x 26.6 = 79.8

, … ,

14 x 26.6 = 372.4

15 x 26.6 =
399
W/m2.

The difference of
the observed mean F value and the prescribed F0
= I × 26.6 value is F – F0 = Δ.

That is, each of the
flux components will be described by a
triplet: (F, F0, σ), or, equivalently: (F,
Δ, σ).

It is evident that
such decomposition formally always can be
done. But it is meaningful (or useful) only if delta is smaller than
sigma;
that is, if the proposed F0 values fall into the
±1 sigma range of
the observed F value.

We will see that
this is the case in each examined flux element.

In turn, we propose
the following F0 values for
the above-listed flux elements:

F0
=

1 × 26.6 W/m2 for
SH,

3 x 26.6 = 79.8 W/m2
for
SAA and LH,

6 x 26.6 = 159.6
W/m2 for SAS,

9 x 26.6 = 239.4
W/m2 for
OLR,

13 x
26.6 = 345.8 W/m2 for DLR, and, finally,

15 x 26.6 = 399 W/m2
for ULW.

We are going to
refer to the F0 values as the 'grid position' of
the
given flux element.

In our website we
will list the observed F values and their
attached 1sigma range from several published studies. They might refer
to
different observations, satellite and surface measurement systems and
networks.
Our work is eased by published global energy budget diagrams and
tables, where
these data are collected and compiled.

For example, the
latest diagram by Stephens and L’Ecuyer
(2015) is based on their own earlier diagram (Stephens et al. 2012),
improved
by their own energy and hydrological cycle assessments. We are in a
comfortable
position as we can simply refer to them. There are also well-tabulated
data
sets as Loeb et al. (2015), and Wild et al. (2015); we will use them
too.

As said, we can
construct important further flux parameters
as linear combinations of the above. First of all, the greenhouse
effect
itself, which is the difference of the surface upward LW radiation and
outgoing
longwave radiation, separately for the clear-sky and the all-sky case:
G(clear) = ULW – OLR(clear) and G(all) = ULW –
OLR(all).

It is evident that

G(clear) = ULW –
OLR(clear) = (15 – 10) × 26.6 = 133.0 W/m2, and

G(all) = ULW –
OLR(all) = (15 – 9) × 26.6 = 159.6 W/m2

It is also evident
that

G(all) – G(clear) =
LWCRE.

Further, the
difference of surface upward LW radiation and
downward
LW radiation is called the Net Surface Longwave (NSL) radiation (or net
surface
radiative cooling): NSL = ULW – DLR, also separately for clear and
all-sky. The
Longwave Cooling (LWQ) of an atmospheric column is defined as the
longwave
energy entering from below less that leaving it above and below: LWQ =
ULW –
OLR – DLR. Evidently, they also have inherited ‘0’ values when they are
created
from the corresponding F0 value. And there are
‘normalized’
quantities, like g = G/ULW, hence there is also a g0.

*

There are also
non-observable
flux components in the system which can only be computed; here one is
independent, the longwave
radiation
in the atmospheric window, which originates from the surface as upward
emission
and reaches TOA in the mid-infrared ‘window’; called therefore Surface
Transmitted Irradiance, STI.

Two can be composed:
Longwave
Atmospheric Absorption:

LAA = ULW –
STI

and a quantity can
be called
Cooling-To-Space, which is the upward emission from the
atmosphere:

These are the basic
components we are going to deal with in
this study. Again, OLR(clear) and DLR(clear) are observed, STI(clear)
is
computed. We present also these clear-sky values in triplets, assigning
an F0(clear)
to them as F0(clear) = I × UNIT(clear); for
example, OLR0(clear)
will be 4 x UNIT(clear).

Our results in this
website are given in flux numerical
tables, and also compiled into a new global energy budget diagram and
poster.

If you are
interested in some preliminary theoretical
considerations, to set the context, read the Introduction; if
not,
just jump to
the Results – or even to the Summary.

Abstract

Surveys
in Geophysics published a special issue in 2012, titled
'Observing and Modeling Earth's Energy Flows'. Kato et
al. give
uncertainty estimate
of surface irradiances, computed with MODIS-, Calipso- and
CloudSat-Derived properties. The best value and uncertainty (1σ)
of
the annual global mean surface Downward Longwave Radiation is DLR = 345
± 7 W/m2; and of the annual global mean surface Upward LongWave
radiation is ULW = 398 ± 3 W/m2. Trenberth and Fasullo, while tracking
Earth's energy, give a mean value of Outgoing Longwave Radiation as OLR
= 238.5 W/m2. Stevens and Schwartz refer to the data of NASA CERES
(Clouds and the Earth's Radiant Energy System) EBAF (Energy Balanced
and Filled) product, which gives a Long-Wave Cloud Radiative Effect,
LWCRE of +26.5 W/m2. — First we observe
here that the above-given mean values of DLR, ULW and OLR are integer
multiples of the referred LWCRE, far within to their 1σ
uncertainty
range: DLR = 13LWCRE (+0.5 W/m2), ULW = 15LWCRE (+0.5 W/m2), OLR =
9LWCRE (+ 0.0 W/m2).
— In the light of latest observations, Stephens
et al. (2012, Nature Geoscience) give an update on Earth's energy
balance, with very similar mean flux values (ULW = 398, DLR = 345.6,
OLR = 239.7 W/m2), with higher uncertainties (±5, 9, 3 W/m2,
respectively), and present also clear-sky values as OLR(clear) = 266.4
W/m2 and DLR(clear) = 319 W/m2; LWCRE is 26.7 ± 4 W/m2 there. — Based
on the same satellite product, Wild et al. (2015) tabulate the CERES
values as ULW = 398.8, DLR = 345.3 and OLR = 239.8 W/m2, and propose
estimate of
the
absorbed shortwave fluxes as Absorbed Solar
Radiation, ASR = 240 ± 2 W/m2; Solar Absorbed by
Atmosphere, SAA = 80 ± 6 W/m2,
and Solar Absorbed by Surface as SAS = 160 ± 6 W/m2. Loeb et al.
(2015), reviewing a longer time period of CERES observations, suggest
again practically the same values. — We realize
that
SAA = 3LWCRE (+0.5 W/m2) and SAS = 6LWCRE (+1 W/m2); both are again
far within to the given uncertainty ranges. — With special focus on the
NASA Energy and Water Cycle Study (NEWS), Stephens and
L'Ecuyer (2015) present an objectively optimized estimate of the
turbulent
heat flows of the energy budget: Sensible Heat (SH) and Latent
heat (LH) fluxes are
given as SH = 26 ± 5 W/m2 and LH = 82 W/m2. — We recognize
that both of these fluxes fit into the structure as SH = 1LWCRE (– 0.5
W/m2) and LH = 3LWCRE (+2.5 W/m2), again with a much
smaller difference
than
the acknowledged uncertainty estimates. — In our study we show
that all the atmospheric
energy flow elements F can be written
as F = F0 + ΔF, where F0
= I × U; here I is an integer, U is a unit flux, and ΔF is a deviation
of the observed F flux value from its prescribed F0
position. We
present the F0
flux values in three different units: (i) for the global
average
all-sky
fluxes, the unit flux is the Long-Wave Cloud Radiative
Effect, LWCRE (termed also the greenhouse effect of
clouds);
(ii) the cloudy unit is
LWCRE/β, where β is cloud area fraction; and (iii) the clear-sky unit
is the atmospheric
window
radiation
(called also surface transmitted
irradiance,
STI(clear)). The ΔF
valuesare well
within the ±1σ range. — We point out definite internal relationships
between these energy flows; the
primary relations indicate: (a) the sum of the energy flows at the
atmosphere's lower boundary (Earth's surface) appear to be
unequivocally connected to the energy
flows at the atmosphere's upper boundary (top of the atmosphere),
separately to the clear-sky and the all-sky case; (b) the greenhouse
factor
has a given position in the structure at g(clear) = 1/3
and g(all) =
2/5; (c) the total
cloud area
fraction seems to be constrained at the value of the planetary
emissivity at 3/5; and (d) even
Earth's
planetary albedo appears to have a preferred value of α = 1 –
√2/2 =
1 – sin 45°. We
start our study with a preliminary hypothetical
explanation on the possible physical mechanism. Note that the
validity of the found relationships does not depend on the
validity of the proposed conceptual framework. Our
results are compiled into a new energy budget diagram and poster.

"

Out
of love for the truth and from desire to elucidate it, Miklós
Zágoni intends to defend the following statements and to dispute on
them in
that place. Here are my 95 theses.

"

Introduction

We
examine the provocative question:

Are
global average radiative and non-radiative flux components in the
Earth's atmosphere constrained and quantized?

Content
of the Introduction:

I.
II.III. IV.V.
VI.

A
conceptual framework
Checking the model the on all-sky CERES data
Deduction of the surface energy budget
Checking the model on the latest published energy budget diagram
Checking the energy budget relationship on the latest published diagram
A quasi-conclusive deduction of the fluxes

I.
A conceptual framework

1.
§ "Global
warming" is the consequence of more infrared absorption in
the atmosphere by more CO2. More absorption means
less escaping
surface emission in the "atmospheric window". Recent longwave radiative
transfer computations clearly show the role of these atmospheric
infrared-absorbing
gases:

When the so-called water vapor continuum is included in the
computation, the longwave
emission reaching to top of the atmosphere from the surface through the
mid-infrared window of the cloudless atmosphere, in global
and annual mean, is 66 W/m2; and it is 99 W/m2
when the continuum is excluded. This is the numerical result
of Costa and Shine
(2012); they use the term "surface
transmitted irradiance", STI, for the
atmospheric window radiation.

Clouds
are not transparent in the infrared,
therefore the global average "all-sky" radiation in the window is
STI(all) = STI(clear) × (1 – β); having the real case with the
water
vapor
continuum absorption and with the observed cloud area fraction of β
~ 60%, we have for the all-sky atmospheric window radiation a value of
STI(all) =
26.4 W/m2. With
this, they updated the result of Kiehl and Trenberth
(1997)
(which served the basis for the 2001 and 2007 IPCC reports), who used
99 W/m2 clear-sky and 40 W/m2 all-sky atmospheric window radiation in
their famous diagram; Trenberth and
Fasullo (2012), and all other energy budget studies published
later accepted this update:

Trenberth
and Fasullo (2012) Fig. 1, with the original figure legend.374 W/m2 is
absorbed by the atmosphere and clouds from 396 W/m2 upward longwave
surface radiation, and only 22 W/m2
escapes to space through the atmospheric window.

Costa and Shine (2012) note
about their result that about "one-tenth of the OLR originates directly
from the surface".We
can add: this
also means that only one-fifteenth of the surface
emission can get through the atmosphere in the window without being
absorbed, since the
upward longwave (ULW) emission from the surface is about 398 W/m2. Data
uncertainties are about ± 5 W/m2. (TF2012 use 22 W/m2 for all-sky
atmospheric window, based on a slightly higher cloud area fraction from
an earlier data set. We will examine this question later in detail.)

Our
atmosphere is really not very transparent in the infrared; where there are
clouds, it is effectively opaque, and where are no clouds, it is still
rather close to be opaque.

For the terrestrial upward
longwave radiation,
the Earth's atmosphere is partially transparent,
but it is not too far from being entirely opaque.

In the all-sky mean, 94 % of the surface longwave
emission
is absorbed by the greenhouse gases
(H2O, CO2, CH4,
ozone etc.), and only
6 % gets through and reaches the
top-of-the-atmosphere (TOA) in the 'window'.

If there is more CO2
(or H2O or methane)
in
the air,
the longwave absorption will increase, hence the surface
transmitted longwave irradiance
is expected to decrease: the window becomes even
tighter, so our atmosphere becomes even less infrared-transparent.

This
is the best
explanation science can offer today: we should take care of the window,
we must keep it open.

If this is so, the concerns about the increasing
atmospheric
CO2-content should be taken seriously.

*

But.

*

The gap between the 'closed'
model and the actual
situation of Earth's atmosphere is so narrow that the following
approach does not seem implausible: just for
curiosity, let us try to
understand this '94 % closed' atmosphere from the 'end of the road',
when
the gap is completely filled; when the whole spectrum of
the terrestrial emission is covered; that is, when 100 % of the
upward longwave surface radiation is blocked by
the
atmosphere and 0 % is transmitted from the surface to space
(STI =
0).

This imagined state can easily be
treated by a simple
greenhouse model of a planet closed into a 'glass-shell'.A basic
textbook example for this case is Figure 2.7 from John Marshall
and Alan Plumb: Atmosphere, Oceans and Climate Dynamics, Elsevier 2008,
Chapter 2: The global energy balance.

Here
it is assumed that
all the incoming solar radiation gets through the atmosphere and
reaches the surface (that is, the 'shell' is completely transparent in
the shortwave); and all the longwave surface emission is
absorbed
by the atmosphere (that is, the shell is 100 % opaque in the longwave). It is also
assumed that no turbulent heat is transferred from the surface
to the atmosphere: sensible
and latent heating (SH and LH) are zero.

This
'glass shell atmosphere' is assumed to be entirely transparent to the
solar flux, but absorbs the longwave upward radiation from the ground
completely. As a single-layer shell, it
will then radiate the absorbed energy upward and downward
equally:

OLR
= DLR

The
constraint here is that in equilibrium the Absorbed Solar Radiation is
balanced by the Outgoing Longwave Radiation (OLR):

is
then equal to OLR in this model; therefore the normalized greenhouse
function, g = G/ULW is also equal to
g = 0.5.

*

How
does this all looks like on Earth?

Here
the case is different. Our atmosphere is only partially transparent to
the solar flux: Solar
Absorbed by Atmosphere (SAA) is not zero, therefore Solar Absorbed by
Surface (SAS) is less than the total solar absorption: SAS = ASR – SAA.
Also, our atmosphere is leaky, that is, only
partially opaque to the terrestrial flux, as we have seen above.

Let
us check first the clear-sky part of the atmosphere. We cite
here the data from the most recent NASA CERES (Clouds and the
Earth's Radiant Energy System) satellite
observations, as presented in the EBAF (Energy Balanced And Filled)
products, see the latest edition Ed2.8 on the NASA
CERES website. For the ten-year period 2000 - 2010, as given
in the 2015 summary:

To
compare it with 2OLR(all), the difference is +28.2 W/m2, and to compare
it with 2OLR(clear), the difference is -24.2 W/m2.

These values are similar to what is lost
in the all-sky atmospheric window — far within to the
measurement
uncertainties.

Let us accept for a moment, at least numerically, that

E(SFC, all) =
2OLR(clear) – STI(all).

Now THIS
relationship would be intelligible.

It would mean that:

The
Earth's
all-sky atmosphere works like an LW-opaque closed shell,
except one-fifteenth of the surface irradiance,
which is escaping to space through the
all-sky atmospheric window.

As
Marshall and Plumb (2008) show in the model:

Here we know from the data that the
fraction of terrestrial
radiation upwelling from the ground which is being absorbed by the
atmosphere is ε =
374/396 ~ 14/15;
that is, 1/15 of the terrestrial LW emission is transmitted
through
the atmosphere.

To close our atmosphere in the LW, only 6 % of the surface
black-body radiation must be grabbed at.

***

Here
another quantity will be taken into account: the difference of
clear-sky and
all-sky outgoing radiations, OLR(clear) – OLR(all), called the
Long Wave Cloud Radiative Effect, LWCRE; it
is
known also as the 'blanketing effect' of the clouds
(in contrast to their shielding effect in the shortwave).

Further, in the
clear-sky Earth, the absorbed solar radiation is not equal to the
outgoing radiation:
ASR(clear) ≠ OLR(clear).
But, as we have seen, the clear-sky window radiation is 66.5 W/m2.
This means that the atmospheric upward emission (cooling-to-space, CTS)
in the clear-sky atmosphere is

THE CLEAR-SKY
GREENHOUSE EFFECT IS
UNEQUIVOCALLY PREDETERMINED BY OLR(CLEAR).Contrary
to all of the internal differences, the logic works:

The Earth's clear-sky atmosphere
maintains a vertical structure where the surface
emission is
twice the atmospheric
LW emission to space,
and where the sum of the surface energy flows is
twice the TOA outgoing radiation;
just as in the closed-shell geometry..

Later we will see that, according to the data, the same is
true for the cloudy part
of the atmosphere as

Absorbed
solar is more than outgoing longwave radiation in the clear-sky part,
and there is evident latent heat exchange between the clear and cloudy
regions. Still, the whole system maintains the "closed shell" geometry.
OLR(clear) = 2G(clear)
is equivalent to

Let's see some logical consequences of this geometry: are they valid in
the observations?

How
the internal energy flows would behave within this
closed-box model?

It
can be anticipated that the fluxes
exhibit a wave-like, periodic character, with 'wave numbers' which are integer multiples of a unit flux
of
LWCRE, when propagating in the 'box' between the two
boundaries; like
in the animation below:

We
check the fluxes from the latest published global energy balance
diagram:
Stephens and L'Ecuyer (2015): The Earth's energy balance(Atmospheric
Research 166: 195–203)

An important energy flow component, clear-sky outgoing radiation,
OLR(clear) is not displayed here, but we recall the earlier published
energy balance diagram by the same authors (Stephens et al. 2012: An
update on Earth's
energy balance in light of the latest observations, Nature
Geoscience 5:
691-696), where the quantity is
presented as:

OLR(clear) (Clear-sky emission) = 266.4 ± 3.3 W/m2

Another fundamental
components presented in the Stephens et al. (2012) diagram are cloud
longwave effect at
top-of-atmosphere and at surface:

LWCRE (TOA) = 26.7 ± 4 W/m2
LWCRE (SFC) = 26.6 ± 5 W/m2

We
can see that the following F flux mean values
in the diagram are
INTEGER
MULTIPLES
OF LWCRE

(the relative uncertainty and the
difference is also shown):

Table
I. Fluxes, according to Stephens and L'Ecuyer (2015):

F

W/m2

1σ
(W/m2)

F0
= I
× LWCRE (W/m2)

Δ
(W/m2)

σ / LWCRE
(%)

Δ
/ LWCRE
(%)

ULW

399

± 5

15
× 26.6

+ 0.0

18.8

0.0

DLR

344

± 1 (?)

13
× 26.6

–
1.8

3.8

6.8

OLR

240

± 4

9
× 26.6

+ 0.6

15.0

2.2

LWQ

–185

± 9

– 7
× 26.6

+ 1.2

33.8

4.5

SH

26

± 5

1
× 26.6

– 0.6

18.8

2.2

E

82

± 7

3
× 26.6

+ 2.2

26.3

8.3

SAA

77

± 8

3
× 26.6

– 1.8

30.0

6.8

SAS

163

± 6

6
× 26.6

+ 3.4

22.5

12.8

Each of these values appear well within the respective uncertainty
range; the only
exception is DLR, but the displayed ±1 W/m2 uncertainty in this figure
seems too
narrow (in the 2012 diagram of the same authors a more
realistic error range of ± 9 W/m2 was
attached to this quantity;
the mean value there was 345.6 W/m2; our 13
× 26.6 = 345.8 W/m2 differs from
this only by 0.2 W/m2).

Below in this
website we examine four
publications and prove that the same quantized
character appears, with very small differences (Stephens
et al. 2012, Stevens and Schwartz
2012, Wild et al. 2015 and Loeb et al. 2015).

So far we were talking about the observable
flux components of the global energy budget. But will the
non-observable flux components like
atmospheric window radiation, which can only be computed, fit into this
whole-number structure?

From
the most recent independent detailed line-by-line computation on
realistic atmospheric profiles presents, a result
of STI(clear)
= 66 W/m2 was published (Costa and Shine 2012).

NASA CERES satellite observations
show a total
cloud area fraction of β ~ 0.605 for the past seven years. For an
IR-opaque single-layer effective cloud area fraction we use β
= 0.6.
The resulted all-sky window
radiation is then STI(all) = (1 – β) × STI(clear) = 0.4 × 66 = 26.4
W/m2. If we used the observed mean value of β
~ 0.605, we would have STI(all) = 0.395 × 66 = 26.1 W/m2.

Remember, these values are from CERES data; the CERES LWCRE was 26.2
W/m2. Our supposed

LWCRE
= (1 – β)
× STI(clear) = STI(all)

equality seems working well.
So we accept STI(all) as a further independent element
in the table, with a value of
STI(all) = 1
× LWCRE, and with a deviation of about ± 0.5 W/m2 or less.

Assuming that STI(all) = 1, these
components in turn will be: CTS(all) = 8,
and CTS(atm) = 7.
Finally, for clear and all-sky conditions, the portion of surface
upward LW emission (ULW) which is absorbed in the
atmosphere is the Longwave Atmospheric Absorption (LAA).
LAA(all) = ULW – STI(all) = 14.
Summarizing
these all observable and non-observable fluxes into a table, they form
an arithmetic sequence with a
common difference of LWCRE:

Table
II. All fluxes, F0 = I × LWCRE (W/m2)

Flux

Name

I

F0

F

LongWave Cloud
Radiative Effect

LWCRE

1

26.6

Sensible Heating,
all-sky

SH(all)

1

26.6

Surface Transmitted
Irradiance, all-sky

STI(all)

1

26.6

Net Surface
Longwave radiation, all-sky

NSL(all)

2

53.2

Evaporation (Latent
Heating), all-sky

LH(all)

3

79.8

Solar Absorbed by
Atmosphere, all-sky

SAA(all)

3

79.8

Turbulent heat
flux, all-sky

(SH + LH)(all)

4

106.4

Greenhouse effect,
clear-sky

G(clear)

5

133.0

Greenhouse effect,
all-sky

G(all)

6

159.6

Solar
Absorbed by Surface, all-sky

SAS(all)

6

159.6

LongWave Cooling,
all-sky

LWQ(all)

–7

-186.2

Cooling-To-Space,
atmosphere

CTS(atm)

7

186.2

Cooling-To-Space,
all-sky

CTS(all)

8

212.8

Outgoing Longwave
Radiation, all-sky

OLR(all)

9

239.4

Outgoing Longwave
Radiation, clear-sky

OLR(clear)

10

266.0

Downward Longwave
Radiation, clear-sky

DLR(clear)

12

319.2

Downward Longwave
Radiation, all-sky

DLR(all)

13

345.8

Longwave
Atmospheric Absorption, all-sky

LAA(all)

14

372.4

Upward LongWave
emission by the surface

ULW

15

399.0

all within about ΔF
= ±3 W/m2 (see the detailed all-sky andclear-skytables with the
uncertainties and deviations later).
Now the F radiative and non-radiative, observable and only-computable
energy flows in Earth's surface and atmosphere seem to follow the
"wave-in-a-box" model: they are integer multiples (I) of a unit
flux of LWCRE:

F = I × LWCRE + ΔF

The basic energy balance relationships:

E(SFC, all) = 2OLR(clear) - LWCRE =
2OLR(all) + LWCRE

ULW = 2CTS(all) -
LWCRE = 2CTS(atm) + LWCRE

*

The
observed cloud area fraction, beta is very close to the planetary
emissivity (defined as the ratio between outgoing LW radiation,
OLR(all) and surface upward LW
radiation, ULW, see e.g Bengtsson 2012), called
also all-sky transfer function, f(all).
Again, with the F0 quantities,

β = OLR(all) / ULW = f(all)
= 9/15
= 0.6.

Formally, the all-sky transfer function f(all) is equal to
(1 – g(all)),
where g(all)
is the normalized all-sky greenhouse function, defined as

g(all)
= G(all)/ULW = (ULW – OLR(all)) / ULW =
6/15
= 0.4.

Consequently, the cloudless
area of the surface, (1 – β),
would be numerically equal to the all-sky greenhouse function g(all).Remember:
both the planetary emissivity (transfer function) and the greenhouse
function of the closed-shell model were 0.5.

On Earth,
where one-tenth
of the clear-sky emission is a 'lost-in-space' surface radiation
through the open
all-sky atmospheric window, we
are not surprised to have

f(all)
= 5/10 + 1/10 = 0.6g(all)
= 5/10 – 1/10 = 0.4The
sharp values of these
quantities are extremely implausible, unless some planetary-level
determinations work in the physical background — or in the geometry. We
should regard them annual global mean 'preferred' values,
around
which oscillations (vibrations, fluctuations, natural
or triggered variations)
are possible — unknown in size and time-scale.

But
according to the above-cited, observed and published data, these
equalities stand very
precisely — at least far within to the accuracy of the observations.
This forces us to take our box model
seriously.

*

For
a little break, notice the following fractions:

G(all)
/ OLR(all) / ULW = 6
/ 9
/ 15
= 2 / 3 / 5

and

G(clear) /
OLR(clear) / ULW = 5
/ 10
/ 15
= 1 / 2 / 3.

Later we will see that the clear-sky
fluxes can be expressed also in clear-sky units as:

A
lot of detailed relationships between the flux elements (like the ratio
of non-radiative to radiative cooling of the surface, and others),
separately for the clear-sky and the cloudy atmosphere, are in several
parts of the Discussion.

*

Several further interesting internal relationships show
themselves in the box-model; to mention only one:

The
cloud-covered part of the surface, β,
radiates the amount of energy β
× ULW,
which is equal
to the all-sky outgoing LW radiation OLR(all):

β
× ULW = OLR(all)

*

V.
Checking the energy budget relationship on the latest published diagram

5.
§ Here we point out that the relationship, which connects
unequivocally the energy budget of the lower boundary (surface) to the
energy flows at the upper boundary (TOA), is THERE in the Stephens and
L'Ecuyer (2015) diagram.

According to these data sets, the energy flows at the lower boundary of
the box (surface) really appear
to equilibrate to the energy flows at the upper boundary
(TOA).

***

VI.
A quasi-conclusive deduction of the fluxes

6. § Let
us survey what we already know about the fluxes in our specific
leaky-but-still-closed box model,
based on Table II.

Number TWO
in the E(SFC) = TWO
OLR surface energy balance equation of the shell
model is an INTEGER,
not a good approximation of a real number. It is a necessary
consequence from
the geometry.

Also,
TWO is an integer is E(SFC, Earth, clear) = TWO OLR(clear). From
here, TWO is an inherited integer in the equality TWO CTS(clear) = ULW.
It
follows that TWO G(clear) = OLR(clear), and TWO STI(clear) =
G(clear).

In the 'leaky' all-sky mean, we then must have TWO
CTS(atm) = LAA(all), which gives, by definition, TWO CTS(atm) = ULW –
ONE STI(all); and again by definition, TWO CTS(all) = ULW + LWCRE. The
surface energy balance equation is TWO OLR(all) + LWCRE = TWO
OLR(clear) – LWCRE = E(SFC, Earth, all), and from here, all the
components in E(SFC, Earth, all) will have their INTEGER factor; for
example, TWO OLR(all) = ULW + THREE LWCRE, and TWO OLR(clear) = ULW +
G(clear).

*

At
the upper boundary (top-of-atmosphere, TOA) there are NINE units in the
all-sky outgoing radiation, from which EIGHT units are emitted upward
from the atmosphere and
clouds, and ONE unit is transmitted from the surface. This ONE unit is
gained back by
ONE unit of longwave cloud effect.

At the lower
boundary (surface, SFC) there are TWO units of net surface longwave
(NSL) radiative cooling and FOUR units of non-radiative cooling
(sensible + latent heat release, SH + LH) (with an internal
distribution of ONE unit of thermals and THREE units of evaporation).
The
surface net
radiative and non-radiative
cooling is then, together, SIX
units.

These SIX units of surface net
and non-radiative cooling are
equal to the SIX units of solar radiation absorbed by the surface
(SAS), which
serves the SIX units of longwave energy content of the greenhouse
effect (G).

These SIX units of the greenhouse effect, added to net
NINE units
coming back from the atmosphere, form the FIFTEEN units of gross surface
radiative cooling (ULW).

This FIFTEEN
units
of the gross surface radiative cooling, with the
FOUR units of surface non-radiative cooling form the NINETEEN units
of the total energy release from the surface E(SFC, out) = ULW
+ (SH + LH).

This THIRTEEN units in
downward longwave radiation, added to the
SIX units of solar radiation absorbed by the surface form
the NINETEEN units
of the total energy income of the surface E(SFC, in) = DLR + SAS.

Having FOURTEEN units of longwave
atmospheric absorption and SEVEN units in non-longwave atmospheric
absorption, we have TWENTY ONE units for the total atmospheric
absorption.

From
these TWENTY ONE units of atmospheric energy income, EIGHT units are
emitted upward by the atmosphere and clouds (CTS(all)), and THIRTEEN
units are
emitted downward to the surface (DLR).

This means that SEVEN units are
emitted upward by the atmosphere only, and TWELWE units are emitted
downward without the cloud longwave effect, leaving TWO units of LWCRE
up and down.

The
TWENTY ONE units in the gross atmospheric energy absorption is then
equal to NINETEEN units coming from the surface, plus THREE units
coming
from solar atmospheric absorption, less ONE unit of surface radiation,
as STI is running through the atmosphere without being
captured.

This
TWENTY ONE units in the atmospheric energy content are then equal to
NINETEEN units of the gross surface energy content plus ONE up and ONE
down longwave
cloud radiative effect.This TWENTY ONE
units of atmospheric energy
content act like a shield of TWO times TEN units of OLR(clear), plus
ONE unit of LWCRE.

The NINETEEN units of surface energy content is equal to TWO times TEN
units of OLR(clear), less ONE unit escaping
in the all-sky
atmospheric window.

The NINETEEN units
of surface energy content is equal to TWO times NINE
units of OLR(all), plus ONE unit of longwave cloud effect.

The
SEVEN units of net atmospheric longwave cooling joins to TWO units of
net
longwave cooling coming from the surface, to form the NINE units of the
total thermal cooling of the system: the outgoing longwave
radiation.

From
this TWENTY units of clear-sky surface energy flows ONE unit is lost in
the all-sky mean, leaving NINETEEN units for the all-sky surface energy
budget: E(SFC, all) = 2OLR(clear) – STI(all), gained back by ONE unit
of the longwave cloud effect: E(SFC, all) = 2OLR(all) + LWCRE.

The
cooperation between the clear-sky part and the all-sky energetic
requirements is created
by a partial cloud cover; with a total single-layer IR-opaque effective
cloud area fraction β
= (NINE units of OLR) / (FIFTEEN units of ULW) = 9/15 = all-sky
transfer function = 0.6 = planetary
emissivity.

*

TEN units of clear-sky outgoing longwave radiation contribute to the
all-sky global average with an area-weighted value of (1
– β) × OLR(clear) = FOUR units. Therefore, the cloudy part
contributes to the NINE units of all-sky OLR with FIVE units, having a
nominal outgoing longwave radiation above clouds OLR(cloudy) = FIVE
/ β
.

Okay then, but we said at the beginning
of this Introduction: "If there is more
CO2
in
the air,
both the clear-sky and the all-sky
surface transmitted longwave radiation
is expected to decrease: the window becomes even
tighter." What's
happening with the window if there is more CO2 in the air? The latest
NASA AIRS instrument has actually measured the decrease in IR energy
from the Earth as CO2 in the atmosphere has increased. This is
observational evidence that increased CO2 reduces the rate of loss of
IR energy to outer space. But we have also observational evidence that
the whole flux structure still maintains the integer ratio system and
that the greenhouse effect keeps its narrow value at its required
position. What's going on?

It seems that the overall
planetary-level energetic control, which determines the closed-model
geometry, poses effective constraints on the entire radiative transfer
process, and it can be anticipated that the most powerful greenhouse
gas, water vapor could play the leading role, through evaporation,
precipitation, cloud formation and greenhouse effect-regulation. The
given energy flow structure belongs to a very specific, unique annual
global mean vertical temperature distribution. Though one element is
perturbed by anthropogenic emissions, all the other elements together
seem to be able to act as an effective stabilizing feedback network.

*

We
do not have enough data to talk about these fluxes and their
relationships
during transient climatic conditions, under glacial and interglacial
circumstances. We can only
say what we see: that these identities and integer ratios are there in
the data covering the recent decades of accurate satellite
observations; some of them are almost exact, and all of them are
surprisingly
close.

It
is remarkable that, contrary to the above-referred AIRS observations,
the two substantial boundary
radiative fluxes, OLR
and ULW fit the best: with 0.2 W/m2 and 0.0
W/m2 deviation into the integer structure. We
regard this as a strong indication that the box model might be valid.

It
is to be emphasized also that we are finding ratios and
relationships
between energy flows, not absolute
values of flows: the all-sky unit is
relative to OLR(all), the clear-sky unit is relative to OLR(clear).

***

An uneasy note on terminology.

When
we mention 'quantized', we evidently do not mean the precisity
of atomic quantum levels. We just wanted to express that 'not
continuously changing'. For example, using the observed and published
data from the tables
above: as long as OLR(all) = 239.4 W/m2, DLR(all) cannot be, say, 360
W/m2, but must be 345.8 W/m2; and ULW cannot be 408 W/m2, but must be
399 W/m2 — without knowing of course how far and
how fast the climate
could deviate from, or fluctuate ('vibrate') around, these integer
relationships.
Originally
we tried to use the word 'periodic', and called our tables 'flux
periodic tables', in the sense of Merriam-Webster: 'ocurring or
recurring at regular intervals'; 'consisting of or containing a series
of repeated digits'; periodicity: 'the quality, state or fact of being
regularly recurrent'; a near antonym of 'continuous'. A British friend
of us supported this notion; but then two of our American friends
practically forbade us to use this ("NOT periodic !!!").

Not
being a native English speaker, we are lost here. We simply
mean
that
the energy flow 'quantum' is one LWCRE in the closed box, being equal
to OLR(clear)/10,
and the flux
values are integer multiples of this. Use 'pattern', 'wave
number', 'arithmetic
sequence' or 'progression' if you wish. Physically think of the
wavelengh of a wave propagating in a box, or anything that cannot
change continuously but exhibits discrete, 'quantized' character.

Once
we were trying to use the expression:
"The global energy flow system
has an internal structure." Now that was a big mistake! We were sent
books from the UK about 'structures': "What kind of internal structure
an
atmospheric energy flow might have?!" So we abandoned that idea
too...

The
same with 'constrained'. One of our friends proposed to use this word,
another fiercely opposed, and suggested 'equilibrated' instead, like:
"The
surface energy flows are equilibrated to the energy flows at
TOA." This might be correct.

We simply mean that, according to the published data:

F
= I × LWCRE + delta F, where I is an integer, LWCRE =
OLR(clear)/10, and the little delta is smaller than the standard
deviation σ.

and:

E(SFC, all) = 2OLR(all) + LWCRE, etc.

The take-away message here is this: you are asked to focus on
the numbers.
They
carry our primary
message; do not let our immature terminology to distract your
attention.

***

So we state three
substantial findings here:

I. The surface energy budget is constrained to the energy flows at TOA
II. There is a discrete pattern in the fluxes
III. The above two features can be explained by a specific
closed-model analogy.

These three, inter-related results give us enough confidence to state
the followings:

This particular,
constrained and quantized
characteristic of
the atmospheric energy flow system is a completely different paradigm
from
the
prevailing climate theory, which expects increased greenhouse effect
from the increased CO2 content of the atmosphere:

Slide #59 from
the presentation of M. Wild (2015a): Energy Cycles in the
global climate system.

If the
above-presented numerical relationships are long-standing and validand the Earth
really maintains the said closed-system character,then this increase
in the greenhouse effectcannot happen.

Let this justifiable forecast be the bottom line of
this Introduction.

***

We continue here
with a History,
where you
can find all the published global energy budget diagrams, to track the
evolution of our knowledge of the individual energy flow components in
the global
energy budget.
In the Discussion we examine several details
of our findings and show
numerous
internal relationships
between
the separate clear-sky and cloudy-sky flux components.
We try also try to
track the energy flow routes
through the climate system, where each part of our diagram is
discussed. In the Results
section we present the clear-sky,
the all-sky and the cloudy flux tables;
for comparison,
a closed model tableis
also presented. We
compile
our findings in a new global energy budget
diagram, built into a detailed
informative energy budget poster, which you can download and
examine in high-resolution.Alternatively, you
can jump to the Conclusions, or directly to the Summary.Our basic numerical
results were
published in the paper: A new diagram of Earth's global
energy budget; this
website offers conceptual context and upgrade to it.
Please send your feedback to info@globalenergybudget.com.
Enjoy your exploration into this fascinating world of Earth's global
energy budget.
Miklos ZAGONI

History

Earth's Radiation Budget: The First 20 Years

Though
the golden era of Earth's energy budgets started with the diagram of
Kiehl and Trenberth (1997), we still start with a diagram from almost
100 years ago.

7.§.

Dines 1917

The first known graphical representation of
Earth's global energy budget is from William Henry
Dines (1917)
The heat balance of the atmosphere. Q. J. R. Meteorol. Soc. 43: 151–158

8.§.

Rudolf Geiger 1950

Another image is given by
Rudolf Geiger: The climate near the ground, 1950, Harvard Univ. Press:

9.§.

Rudolf Czelnai 1979

Rudolf Czelnai in his 'Introduction to meteorology' (1979) university
lecture notes (in Hungarian)
gives good approximations:

Numbers, they say,
have been rounded for the purpose of illustration.
"Because clouds are bright, their presence increases reflection of
shortwave (SW) radiation by 50 W/m2 (cooling),
while the greenhouse effect of clouds results in a longwave (LW)
warming of 30 W/m2."

It is
only of
historical interest that the Wild et al. 1998 paper, submitted one year
after the KT97 article appeared in the BAMS 1997 February issue,
proposes sevaral updates without even referring to it.

12.§.

The diagram in the UN IPCC 2007 Fourth
Assessment Report.
It is thought to be identical with the original. But is it? Find the
difference!

(IPCC WGI AR4 2007 Ch 1 Fig 1)

A
new label appears here: 'Emitted by Clouds', attached to the 30 W/m2.
But
the KT97 paper states: "The atmospheric emitted
radiation is apportioned into two parts to show the LWCF of 30 W/m2".
Longwave cloud effect is the reduction
of the clear-sky outgoing longwave radiation, 265 W/m2, to the all-sky
mean, 235
W/m2, in the presence of clouds; and not an individual additive energy
flow component of the all-sky outgoing radiation. And it is far too low
to be the real
cloud-top
emission. KT97 calculate with a ~60%
cloud coverage. This means that the 265 W/m2 of outgoing
radiation belongs to the ~40% cloudless area, with a
contribution to
the
all-sky mean: 0.4 × 265 W/m2 = 106 W/m2. Hence, from
the cloud-covered part of the atmosphere must come the
remaining 235 – 106 = 129 W/m2, instead of 30 W/m2.

Interestingly, this controversial label appears also in the NASA Earth
Energy Budget Poster as well, see later.

Funny
enough that "The Atmospheric
Radiation Measurement (ARM) Program: The First 20 Years",
published in 2016, still uses this 2009 diagram as a basic reference,
despite the fact that its authors themselves published an update to it
in 2012, let alone other upgrades from 2013 and 2015. Wrong window
value, wrong atmospheric LW absorption and emission, outdated LWCRE ...

*

The graphic really
became famous: The
Economics created its own version (with
the expressive title: The clouds of unknowing. Mar 18th 2010):

In
2012 Wild asserted again that DLR must be about 344 W/m2, and, as
TFK2009 accepted,
solar absorbed by surface (SAS) must be about 160 W/m2:

Other
proposed changes are mainly consequences and necessary adjustments
because of this basic change of Back Radiation to 344 W/m2. Very
important: uncertainty estimates (340, 350) also attached. Based on
improved hydrological cycle estimates, the new proposed non-radiative
surface cooling (the sum of the turbulent fluxes: thermals
plus
evaporation) is 17 + 88 =105 W/m2.

15.§.

Costa and Shine (2012):
Outgoing Longwave Radiation due to Directly Transmitted Surface Emission
Costa and Shine (2012) state that the purpose of producing the value is
"mostly pedagogical".
They seem to be too humble. "Atmospheric
Window" is one of the most fundamental quantities:
it describes the
amount of surface irradiance going through the atmosphere and leaving
to space
without absorption.
If you think of the greenhouse effect as
the "heat-trapping capacity" of the atmosphere,
then this is the
quantity that is not
trapped:
it measures the infrared transparency (or
opacity) of the atmosphere.

Its
value in KT97 is given as 40 W/m2, as KT97 calculated the clear-sky
window
radiation to be 99 W/m2,
and, regarding a 60% single-layer LW-opaque
cloud area fraction,
they have 99 × 0.4 ~ 40 W/m2 for the all-sky mean.

But Costa and Shine re-calculated this quantity and found that
KT97 handled the water vapor continuum incorrectly;
their proposed new
value for the clear-sky surface transmitted irradiance is
STI(clear) = 66 W/m2, instead
of 99 W/m2.

Trenberth
and Fasullo (2012) immediately accepted the STI(clear) = 66 W/m2 of
Costa and Shine,
and, having an earlier estimate of cloud area fraction
of 67% from ISCCP 1999,
they assigned a new value to the all-sky window
radiation as
66 × (1 – 0.67) = 22 W/m2 in their new update.

As
a consequence, LW atmospheric absorption became 396 – 22 = 374 W/m2,
and
the emitted by atmosphere upward flux element is now 239 – 30 – 22 =
187 W/m2.
It
can be seen that every value was changed from the original KT 1997
picture,
with the only exception of 30 W/m2, assigned to the clouds.

[ I
beg your pardon? The value of an absolutely essential climate
parameter, "Atmospheric Window", describing the atmospheric
transparency, published in the 2001 and 2007 UN IPCC reports, was halved? From
40 W/m2 of KT97 to 22 W/m2 of TF12 ? — Well, yes ... Actually,
the new value is two-thirds of the original (as the new STI(clear) = 66
W/m2 is two-thirds of 99 W/m2 of KT97), assuming the same cloudiness.
Hence, as the original all-sky "Atmospheric Window" was (1 –
0.6)
× 99 W/m2 = 40 W/m2, now its best value is (1
– 0.6) × 66 W/m2 = 26.4 W/m2.
]

17.§.

What
is this "30" W/m2 after all, attached to the clouds in all of these
figures?
The UN IPCC 2007 diagram says it is “Emitted by Clouds”.
This
label is missing from the original KT97 figure.

But it cannot be
cloud-top emission.
If the all-sky outgoing longwave radiation is 239
W/m2,
and the clear-sky outgoing radiation is 266 W/m2, then,
having a
60% global average annual mean cloudiness,
the contribution of the
clear-sky part is 266 × 0.4 = 106 W/m2.
This leaves 239 – 106=133 W/m2 for
the cloudy part.
So the value of 30 W/m2 as cloud-top radiation is far
too little.

18.§.

Interestingly,
the NASA Langley Center’s Energy Budget Poster from 2014
still contains
this description. And, they didn’t bother to change the atmospheric
window radiation
from the original 40 W/m2 to the newly computed one.
http://science-edu.larc.nasa.gov/energy_budget/
As
we said above, the “Emitted by Clouds” label is not given in the
original KT97 diagram.
Instead, as they say:
“The atmospheric emitted
radiation is apportioned into two parts to show the LWCF of 30 W/m2”.
Here LWCF stands for longwave cloud forcing,
which is defined as the
difference of the clear-sky and the all-sky outgoing longwave
radiation;
and also, the difference of the all-sky and clear-sky
greenhouse effects,
therefore called also the greenhouse effect of clouds.

But
LWCF, defined as above, is the reduction of outgoing radiation in the
presence of clouds;
in itself it is not a contributing component of
all-sky outgoing radiation.
To attach an arrow for it as a composing
element of OLR is not correct.
It is not a part of OLR, either this or
that way.

Maybe this problem was recognized by some authors of the
later published energy budget diagrams,
because there LWCF is not
displayed;
see for example the figure of Stevens and Schwartz
(2012) from the same
Observing and Modeling Earth’s Energy Flows
Special Issue of Surveys in Geophysics,
altough in the text LWCF (as LW CRE) is given from CERES EBAF as 26.5
W/m2.

20.§.

The
only exception where the LWCF is still shown is the diagram in

An
update on Earth's energy balance in light of the latest global
observations

where
ULR is upward LW radiation and DLR is downward LW radiation (emission)
by the atmosphere.
ULR is not given in the diagram (even its arrow into
OLR is also missing);
DLR is 345.6 ±9 W/m2 in all-sky and 319±9 W/m2 in
clear-sky
(LWCE at the surface is given as 26.6±5 W/m2).
ULR ought to
be 565 – 345.6 = 219.4 W/m2 here;
or, repeating the method of KT97 ("to
show the LWCF"), 219.4 – 26.7 = 192.6 W/m2.
This is more than 187.9
with about 5 W/m2, shown as 3±5 W/m2 in the clouds,
but still within
the assigned ±12.5 W/m2 error bound.

The quantity labelled as ‘All-sky longwave absorption’,
with the value of -187.9 W/m2, is the ‘net’ atmospheric absorption:
The
negative sign shows that this ‘absorption’ is an emission:
Eq. (1)
defines actually longwave atmospheric cooling,
which is the sum of the
non-LW
absorption terms:

LWQ = – (SAA + SH +
LH),

being equal evidently to
the net LW emission of the column:
LW radiation entering (from below)
less that leaving it (above and below):

Note
also that with the better window value (22 W/m2),
LAA would be 398 – 22
= 376 W/m2, which is the double of –LWQ = 187.9 W/m2:

LAA + 2LWQ = 0.

This means that the gross longwave absorption of the atmosphere is the
double of its longwave cooling.
Further, let us realize here that another unexplained relationship can
be revealed from the data:

DLR – LWQ = 2OLR(all) + 2LWCRE + IMB = 2OLR(clear) + IMB

within 0.1 W/m2:

345.6 + 187.9 = 533.5 = 2 × 239.7 + 2 × 26.7 + 0.6 = 2 × 266.4 + 0.6,

contrary to the noted ± 9 W/m2 or even ± 12.5 W/m2 uncertainties.

What
does this equality describe?
Total atmospheric LW emission is not a
free variable of the IR-absorber composition of the atmosphere
but
being determined completely by the energy flows at the upper boundary.
We were not able to find any reference or expression of this equation,
either in the paper or anywhere in the literature.

23.§.

Stephens
et al. (2012) Nature Geoscience
PART THREE: Periodicities

It
is easy to realize that surface emission, outgoing radiation and
downward atmospheric emission
(and hence LW cooling, net surface LW
[NSL]
and also the greenhouse effect, both for the all-sky and
clear-sky case)
can be expressed as multiples of the longwave cloud
effect,
far within to the noted uncertainties:

No window
radiation, no
atmospheric LW absorption, no atmospheric upward emission. LWCRE also
missing. This diagram is totally
inappropriate to make any prediction on the future of the planetary
emissivity or the atmospheric opacity.

Some
values are evidently outdated:
atmospheric window is
still from the KT1997 paper,
hence atmospheric LW absorption and upward
emission are also wrong.
No error bounds, problematic decimal numbers, wrong "emitted by clouds".

Letter from the American
Association for the Advancement of Science (AAAS) to the Members of
Congress (June 28, 2016)

"reflects
the scientific consensus represented by, for example, the U.S. Global
Change Research Program, the U.S. National Academies, and
Intergovernmental Panel on Climate Change."

As we have shown
above, the IPCC diagram, as well as their text, is in serious lack of
essential climate parameters: neither window radiation, nor atmospheric
LW absorption, atmospheric upward emission, clear-sky
outgoing radiation or LW cloud effect is quantified.

The case is worse with the other two
references:

UK
Royal
Society - US National Academy of Sciences 2014:
Climate Change:
Evidence & CausesTheir presentation
is unsuccessful, unaccectable, oversimplified.
The diagram is
totally inadequate to explain the greenhouse effect.
No solar
atmospheric absorption, no sensible and latent heat, no clouds ... and
no data.

"Some"
?!

*

27.§.

U.S.
Global Change Research Program
Climate Change Impacts in the United Sates,
Appendix 3: Climate Science Supplement.
None of the
essential parameters are given,
the conclusion is unsupported:

*

28.§.

The same report presents an unfortunate
modification of the Stephens et al. (2012) diagram:

Modified uncertainty ranges (159-165±6, 17-24±7, 80-88±10) make no
sense; the statement in the figure legend:
"It demonstrates that our scientific understanding of how the
greenhouse effect operates is, in fact, accurate"
is not supported.

29.§.

A slightly modified
version of the IPCC 2013 diagram is given in:Wild et al. (2015)The
energy balance over land and oceans

Clim
Dyn 44: 3393–3429

30.§.

L'Ecuyer
et al. (2015)
The Observed State of the Energy Budget in the Early Twenty-First
CenturyJournal of Climate
28: 8319 – 834
An
important effort is presented by L'Ecuyer et al. (2015):
an 'objectively
balanced observation-based reconstruction' of the energy budget is
promised,
where relevant energy and water cycle constraints were
applied on the satellite observations.

They say that in the absence of these
constraints, the observed energy budget looks like this
(see below
their Fig. 1), while the constrained structure is given in their Fig.
4:

The data are presented in a table as well:

31.§.

Stephens
and L'Ecuyer (2015): The
Earth's energy balanceAtmospheric
Research 166: 195–203
But something must have gone wrong with the 'objectively balanced'
first optimization,
since an immediate update became necessary to the L'Ecuyer et al.
(2015) paper
(available online on the same week):

Stephens and L'Ecuyer
(2015) applied an (even-more objectively balanced) 'second
optimization',
where two fundamental energy budget parameters, DLR and LW Cooling,
were
taken back to their original, observed, unconstrained value.

First diagram below: L'Ecuyer et al. with observed and the constrained
data.

The
atmospheric energy balance equation was also 'lost' in the maintime:

The 2014 version:

The 2016 version:

34.§.

Cloud
Area Fraction
Kiehl
and Trenberth (1997) mention a total cloud area fraction of beta = 62%,
but when
computing the all-sky atmospheric window from their clear-sky value as
40
W/m2 = (1 – 0.6) × 99 W/m2,
they calculate with a cloud area fraction of 60%.

CERES
SYN1deg product version Ed3A presents data from March 2000 to April
2016.
It starts with a mean value of about 62%,
then shows a slight decrease
to an average of 0.605 for the last seven years.

***

Kiehl and Trenberth, with beta = 0.62, had an albedo of 0.31.
ISCCP, with beta = 0.67, had the albedo at 0.33 (Rossow and Zhang 1995).Beta = 0.6 is
consistent with a planetary albedo of 0.293.
***
Measurement descriptions mention uncertainties coming from the handling
of cloud overlap:
the actually observed multi-layer cloud area fraction is corrected to
get the single-layer fraction.

***

There are also concerns with objects like haze, fog and very thin
clouds;
these might have more than zero infrared optical depth.

We present here all F fluxes in the Earth's
energy flow system
(solar atmospheric and surface absorptions,
longwave absorptions and emissions,
non-radiative fluxes as sensible and latent heat,
observable and only-computable radiations as window radiation or upward
atmospheric emission)
as

F = F0 + Delta F, where

Delta F is a small fluctuation (due to observation errors or systematic
deviations,
typically within the ±2 W/m2 range, which is less than ±1 sigma),

expresses LW Cooling of the atmosphere
(the LW energy entering into it from below less that leaving it above
and below)
(see e.g.
Stephens et al. 1994: Observations of the Earth's radiation budget; Eq.
9)

with an accurcy of 0.5 W/m2,
contrary to the noted much higher 1-sigma uncertainty ranges.

If the equality

E(SFC) = 2OLR +
LWCRE

proves to be valid, it might modify our concept about the work of the
climate system,
as it suggests that the energy at the surface is not a free variable of
the atmospheric downward radiation,
but being pre-determined by the energy flows at TOA.

It can be written also, within some imbalance as:

E(SFC) = OLR(all) + OLR(clear)

or

E(SFC) = ASR + OLR(clear)

or

E(SFC) = 2ASR +
LWCRE.

*Surveys in
Geophysics released a Special Issue on the Earth's hydrological cycle
in 2014;
it made possible to refine the value of the latent heat, as it is given
there by Bengtsson (2014) as
LH = 80 W/m2.

This value can be written as
LH = 3 LWCRE + 0.5 W/m2,

therefore
SH = 26.5 W/m2 = 1 LWCRE.

which are now another members in the arithmetic sequence of fluxes with
a common difference of LWCRE.

The surface energy is then becomes the 19th member of the progression:

We
are not aware of any mention or reflection to these characteristics of
the energy budget by any of the authors of the Surveys in Geophyscis
Special Issue (2012) or the Stephens et al. Nature Geosci (2012) paper,
or by anyone in the literature.

Below
we repeat the periodic tables and the diagram published there
with some data and structure update.

Note
also that the energy flows at the surface are determined by the energy
flows at
TOA,

E(SFC)
= ULW + SH + LH = OLR(all) + OLR(clear) = 2OLR(all) + LWCE.

It can also be written, within
an imbalance, as

E(SFC) = 2ASR +
LWCRE

or

E(SFC)
= ASR + OLR(clear)

.

***

The atmospheric version of this balance
equation can be recognized numerically in the referredStephens et al.
(2012)
diagram.
This equality does not follow from any known balance
requirement, and is not mentioned either in the paper or anywhere in
the literature; our addition is in a textbox:

*

It can be found,
with their own data, in the NASA
Langley (2014)
poster as well
(our addition: yellow and red arrows and white textboxes).

***

We
have to emphasize that this relationship:

(the strict equality of the total [upward plus downward] atmospheric
emissions
to the total [absorbed
plus emitted] energy flows at TOA,
with or without the LW cloud effect)

is valid in these two different, but coherent and
self-consistent
representations.

***

This
is evidently not
the case, for example, in the CO2-atmosphere of the Mars:

On Earth,
the surface and atmospheric energy budgets are maximized,
and limited (constrained) to (predetermined by)
the available energy at TOA.

***

This fact in itself undermines the
prevailing paradigm
which on Earth assumes increasing atmospheric LW absorption,
increasing upward and downward atmospheric emission, and,
as a consequence, elevated greenhouse effect at the surface,
as a result of increasing greenhouse gases.

***But how? More CO2 won't absorb more?Yes,
they probably try to absorb more, initially and instantaneously perhaps
successfully,
but then the limit of the anual global mean blocks the process and
regulates back to where it was.

Exchange of CO2 and H2O molecules between the atmosphere and the ocean
surface,
and the created vertical and regional temperature configuration
maintain the prescribed energetic construction.

***Before
presenting our flux aritmetic progression
tables, to make it easy to compare them to the observed data,
we show here another data tables from open access publications:

Sigma is taken from Stephens and L'Ecuyer (2015) and
from Loeb (2015)
Delta is taken from two different studies.
STI(all) is computed from STI(clear) = 66.5 W/m2 and β
= 0.6.
LWCRE = 26.6 W/m2 defined from OLR(clear)/10.
Upward atmospheric emission, termed also ATM, is labelled here as
Cooling-To-Space, CTS
CTS(atm) refers to cooling to space by atmosphere, CTS(all) includes
also the cloud longwave effect.

Line 19 says that the energy flows at the
surface are predetermined by the energy flows at TOA.

If
these observed data are correct, it can be seen that the energy flows
at the surtface:

Besides
the all-sky structure, where the unit flux was LWCE = 26.6
W/m2,
there is also a clear-sky pattern, with the unit of
STI(clear) = 66.5 W/m2, see Table 3.

Further, the amount of energy flows at the
surface can be calculated as follows.
Absorbed
solar radiation in the climate system under cloud-free skies,
from
CERES-EBAF, is ASR(clear) = 287 W/m2; higher than the clear-sky OLR of
266 W/m2.
The clear and the cloudy subsets of the atmosphere in
themselves are not in equilibrium;
energy exchange must appear between
the two:
the 21 W/m2 clear-sky surplus in
the all-sky global average means
(1 – β) × 21 = 8.4
W/m2,
therefore 8.4 / β = 14
W/m2 must
appear in the cloudy part..

Using ASR(clear) = 287 W/m2, the best
estimate for the
cloud-free surface atmospheric absorption is

The existence of such a clear-sky structure
was introduced and first presented in the papers of Ferenc Miskolczi.

The
2CTS(clear) = ULW relationship, based on their LBL-computations, was
first recognized by
Miskolczi and
Mlynczak (2004). The whole clear-sky structure, including the
STI(clear) /
ULW = 1/6,
2G(clear) = OLR(clear) and OLR(clear)/ULW = 2/3 realtionships, was
first
presented in Miskolczi (2007).

The above papers propose also an equality of the clear-sky
atmospheric longwave
absorption, LAA, and downward longwave radiation, DLR (under
the controversial
name 'Kirchhoff law', later under the term 'radiative exchange
equilibrium'), hence DLR(clear) also occupies 'position five' in their
clear-sky structure.

The
equality of these two terms would suggest a zero radiation exchange
between the surface and the atmosphere. According to the observed data,
LAA(clear) and DLR(clear) are not equal: DLR(clear)
is 319.2 W/m2 (position 12LWCRE in the all-sky table),
while
LAA(clear) = 332.5 W/m2; the difference is
13.3 W/m2 = LWCRE/2.

Zhang, Rossow, Lacis, Oinas, Mischenko (2004):
Calculation of radiative fluxes from the surface to top of atmosphere
based on ISCCP and other global data sets: Refinements of the
radiative transfer model and the input data.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, D19105,
doi:10.1029/2003JD004457, 2004 *The differences are smaller than the CERES
EBAF TOA flux adjustments:

Global enegy budget, flux progression tables and the greenhouse effect
of
cloudsClick to enlarge.
Bottom lines: the observed F values and their sources.
Right column: F0 values as integer multiples of
three different units.
Top rows: the units and their interrelations.
Left column: the three (all-sky, cloudy and clear-sky) surface energy
balance equations.
The validity of the 'cooling-to-space' approximation, and
some relationships are
detailed.

43.§.

Discussion

In
this section we examine several details of the energy budget.
As they are all interconnected, repetitions are unavoidable.

***

Let
our
first note be here that in our Poster we gave the explanation of
STI(all) = LWCRE from the other direction.

So
far, in the Introduction, we have introduced this relationship from the
closed-model perspective:

the
LW energy being lost in the all-sky atmospheric window
is gained back by the cloud longwave effect.

But
an opposite description is also possible,
if we approach the situation from an energy minimum perspective:

Clouds
cool the surface in the SW, warm it in the LW.
The warming effect, LWCRE, is componsated by an equivalent amount of
energy
being lost in the all-sky atmospheric window.

The
physical principles in the background may be different,
but the resulting structure is the same.

***

In
the followings we confine ourselves to the formal description of
the pattern;
therefore we make only brief comments on the found
arithmetic structure
regarding the proposed F0
values.

44.§.

Surface energy balance

(Here
we repeat some considerations already discussed in the Introduction.)

It
can be seen in the data that:

the
all-sky energy income of the surface (absorbed
shortwave plus longwave downward radiation),
being equal to the total surface
radiative and non-radiative energy loss,
is uniquely determined by (constrained to) the energy flows at TOA:

This
energy radiates equally upward (out to space) and downward (to the
surface).

It is also assumed in this model that there
is no turbulent heat transfer: SH
= LH = 0.

So the surface energy balance reads:

E(SFC) = ULW = ASR + DLR = 2OLR,

As Marshall-Plumb (2008) put it:

Hence
the left-hand side of Eq. (2-8) is E(SFC) = ULW, and the right-hand
side is 2OLR.

***

The
"glass-shell" atmospheric model's periodic table looks like:

SH

0

LH

0

STI

0

SAA

0

SAS

1

ASR

1

OLR

1

CTS
= OLR – STI

1

G = ULW
– OLR

1

DLR

1

LAA =
ULW – STI

2

ULW

2

E(SFC) =
SAS + DLR
= ULW + SH + LH
= 2OLR

2

***

It
can be seen from the data that, within ±0.5 W/m2, our partially
opaque, partially cloudy and turbulent atmosphere, with the
help
of the longwave cloud effect, still maintains a 'quasi-opaque'
greenhouse effect with

E(SFC, clear) =
2OLR(clear)

In
the all-sky case,
STI(all) is "lost through the open atmospheric window":

E(SFC, all) =
2OLR(clear) – STI(all)

but
gained back by the longwave effect of clouds:

E(SFC, all) = 2OLR(all) +
LWCRE.

Hence it is true that

E(SFC, clear) =
E(SFC, all) + LWCRE.

Earth
has a higher
DLR and lower
ULW than in the glass-shell model,

and
the difference in both cases is the turbulent flux:

DLR(all)
= OLR(all) + (SH + LH)(all)

and

ULW
= E(SFC, all) – (SH + LH)(all).

Adding
them together we get:

DLR(all)
+ ULW = OLR(all) + E(SFC, all).

Now
let us realize that the surface energy balance equation of the
glass-shell case
can also be written in the form of:

The
partially SW-transparent, partially LW-opaque atmosphere of the Earth,
with a partial cloud cover, maintains the same 'closed' character
as in the glass-shell greenhouse model, where
the surface energy content is completely determined by the energy flows
at TOA as

E(SFC)
= 2OLR,

but

with
higher DLR (the difference is the SH+LH turbulent flux):

DLR(all)
= OLR(all) + (SH + LH)(all),

and with lower ULW (the difference again is the SH+LH turbulent
flux):

ULW
= E(SFC, all) – (SH + LH)(all),

and

with
a higher surface energy content, E(SFC),

the
difference is one longwave cloud effect, LWCRE,
which is the greenhouse effect of clouds:

E(SFC, all) = 2OLR(all) + LWCRE .

The
clear-sky part of the Earth's atmosphere
reproduces the closed glass shell model as

E(SFC, clear) = 2OLR(clear) ,

and
the surface below the cloud layer works as

E(SFC, cloudy) = OLR(cloudy) +
OLR(clear).

***

The
contribution of the cloudy part to the total
all-sky surface energy is
β × E(SFC, cloudy) = 292.6 W/m2 = 11
LWCRE;

and
the contribution of the clear-sky part is
(1 – β) × E(SFC, clear) = 212.8 W/m2 = 8
LWCRE.

*

47.§.

A
major
consequence for the atmosphere:

E(ATM,
all) =

LAA
+ SAA + SH + LH = CTS(all) +
DLR(all)

=
E(SFC, all) + 2LWCRE

*

48.§.

Here
we examine how the abosrbed solar radiation, ASR, is
distributed into
the clear-sky and cloudy parts.

Their
area-weighted quantities are the same,
and equal to the all-sky net
surface longwave radiative cooling:

133 × 0.4 = 53.2 W/m2

88.66
× 0.6 = 53.2 W/m2

=
2 LWCRE =

NSL(all).

The total net cooling of the
surface is partitioned into
three equal amounts:

the clear and the
cloudy part, separately, cool non-radiatively
with the same amount of energy as the all-sky net LW radiative cooling,
together with a quantity being equal to the all-sky greenhouse effect:

G(all) = 3 NSL(all)
= 6 LWCRE.

*

It
can be seen that in
the all-sky mean,

the greenhouse
effect is double of the all-sky latent
flux:

G(all)
= 2 LH(all)

Under
clouds:

G(cloudy)
= 2 (LH + SH)(cloudy)

In
the clear-sky:

G(clear)
= (LH + SH)(clear).

***

Under
the cloud deck, in the cloud-surface cavity, evaporation is the
dominant effect, convective heat transport is small, or zero, in
average. An interesting
sub-case can be deduced from the SH(cloudy) = 0 approximation.

This
relationship was first displayed numerically in the Trenberth and
Fasullo (2012) diagram,
with a value of 187 W/m2, and repeated closely in the Stephens et al.
(2012) diagram,
where CTS is not shown but LWQ = – 187.9 W/m2.

This
equality expresses the fundamental energetic fact that
the all-sky longwave atmospheric absorption is double of the longwave
cooling:

LAA(all) + 2LWQ = 0.

***

56.§.

Here
we examine in some detail the

"Cooling-to-space
approximation"

The
approximate equality of the cooling-to-space flux gradient and
the
total spectral cooling rate of an atmospheric column for several levels
and gases in a number of climatic situations (tropical,
mid-lattitude, arctic) was first observed under
clear sky conditions by

the
“radiation
cooling at any level is due to the exchange of radiation between that
level and
(a) space, (b) the ground and (c) other levels.”
R&W had suspected that “(a) might be far
the most important term under many circumstances
– a result which, if true,
could lead to enormous simplification of the cooling rate calculation”

["its
importance cannot be overstated", said Goody and Yung 1989,
in the "Radiation exchange with the boundaries" section of their book.]

An
interesting question arises:

how
much are the corresponding flux elements
(the vertical integral of the flux gradients for all gases)
in the annual global mean?

The flux elements are:

"cooling-to-space"
(CTS), the same as "emitted by atmosphere upward" in the
Trenberth-diagrams;
and the total LW cooling of a column (LWQ) in the
Stephens-L'Ecuyer-Loeb diagrams,

the
latter flux element being equal to the LW energy entering from below
less that
leaving it above and below,

LWQ
= ULW – OLR – DLR.

Since
the (c) term (radiation between the different atmospheric levels) is
evidently zeroed out in the integral,
what remains for the difference of CTS and LWQ is the (b) term: the IR
radiation exchange
with the surface.

For
the global averagewe found that

CTS(atm)
= –LWQ and

CTS(all)
+ LWQ = LWCRE.

This
all-sky mean value is a result of compenstaion between the clear and
the cloudy parts of the atmosphere.

It
is evident also that under clear-skies, the (b) term, IR radiation
exchange term with the ground, cannot be zero:
as the atmosphere is always colder than the surface in the annual
global mean
(temperature inversions can act only on regional, or seasonal-temporal
scale as e.g. in the arctic winter),
there must be a net IR radition from the ground to the atmosphere.

How
much is it?

Its
value in the clear-sky part is, as show in our
poster:

LWQ
+ CTS(clear) =

[ULW
– OLR(clear) – DLR(clear)] + CTS(cler) =

[399.0
– 266.0 – 319.2] + 199.5 =

–186.2
+ 199.5 = 13.3 W/m2 = LWCRE/2;

its
contribution to the global average is

(1
– β) × [LWQ +
CTS(clear)] = LWCRE/5 = 5.32 W/m2.

*

In
the cloudy part, with similar calculation,

LWQ
+ CTS(atm, cloudy) =

[ULW
– OLR(cloudy) – DLR(cloudy)] + CTS(atm, cloudy) =

[399.0
– 221.66 – 363.53] + 177.33 =

–
LWCRE/3 = 8.87 W/m2,

and
its contribution to the global averge is

β
× [LWQ +
CTS(cloudy)] = – LWCRE/5 = – 5.32 W/m2.

*

Hence their sum in the all-sky mean is
really zeroed out:

LWQ + CTS(atm) = 0.

We regard this equality as one of our important results which stands on
its own.

***

From
the equality

LWQ
+ CTS(clear) = LWCRE/2,

*using the terms from their definition:

*

LWQ
= ULW – OLR(clear) – DLR(clear)

ULW
= LAA(clear) + STI(clear)

OLR(clear)
= CTS(clear) + STI(clear)

*

it
can be deduced that

LWQ
+ CTS(clear) = LAA(clear) – DLR(clear),

hence
the right-hand side is also equal to LWCRE/2:

*

LAA(clear)
– DLR(clear) = LWCRE/2.

*

Therefore
a hypothetic
equality

LWQ
+ CTS(clear) = 0

would mean

LAA(clear)
= DLR(clear),

but
in
reality, according to the theory and the observed data,
there is a difference between the two,
being equal to the (longwave)
radiation exchange with the ground
in
the clear-sky part of the atmosphere;
this difference is LWCRE/2 = 13.3
W/m2.

That's
why DLR(clear) doesn't have the same position of No. 5 as LAA(clear) in
the clear-sky structure;
but it does occupy position No.12 in the all-sky table, with

DLR(clear)
= 12 × 26.6 W/m2 = 319.2 W/m2.

This
is a correction to our paper, where, based on earlier studies, we
incorrectly inserted DLR(clear) into position No.5 of the clear-sky
table.

*

We
think the
importance of the above relationships in the global energy budget is
that
they establish numerical connections between the observable flux
element of LWQ
(= ULW – OLR – DLR) and a non-observable flux element (which can only
be computed), i.e., CTS.

The
equalities of

LAA(clear)
= DLR(clear) + LWCRE/2

and

LAA(all)
= DLR(all) + LWCRE

serve
as fundamental pillars of the stability of Earth's global
energy
balance; see our diagram.

***

57.§.

The
formalism given by the flux periodic tables helps
us to recognize some further interrelations.

The
cloud-covered part of the surface emits the
energy being equal to
outgoing longwave radiation:

ULW × β0
= OLR(all).

f(all) serves as a mapping of ULW into
OLR(all),

and
by the given cloud area fraction,

ULW
is mapped into OLR(all)
as ULW into the cloud-covered part of ULW:

Evidently
the clear-sky mapping function gives

ULW
× f(clear)
= OLR(clear).

The
all-sky greenhouse function gives

ULW
× g(all) =
G(all).

Note
that the mapping of OLR(clear) into G(all) is:

OLR(clear)
× f(all) =
G(all),

therefore

g(all) = f(clear) × f(all),

see
also below.

*

58.§.

The ratio of the clear and
cloudy areas is

equal
to the clear-sky transfer function:

(1 – β0)
/ β0 = 0.4 /
0.6 = 2/3 = f(clear),

and
the ratio of the cloudy area to the total surface (3/5)
is equal to the all-sky transfer function,

β0 = f(all).

Finally,
the ratio of the clear area to the total surface (2/5)
is equal to the all-sky greenhouse function:

Let
us first realize that the ratio of absorbed
and incoming solar radiation is

ASR/ISR
= 240.2/340 = sin 45° = √2/2,

hence
the albedo,

RSR/ISR
= α =
1 – sin 45° = 1 – √2/2
= 0.293

seems
constrained, symmetrical and very stable.

The
probability for an incoming photon to be reflected rather than absorbed
is therefore

RSR/ASR
= (1 – sin 45°) / sin 45° = √2
– 1.

***

What does it mean that the albedo has also a stationary,
steady-state
position?

Does it mean that it cannot be modified through, say, pouring soot on
the ice and snow?

Evidently, if we paint white surfaces black, it will modify the albedo.

If a grid position really exists, it would mean that the whole
system has an energetically preferred state,
a 'propensity' to
occupy that position on the long run.

The hows and whys are not yet known;
let us recall that the above-cited paper refers to 'Gaia' when the
'regulation' comes into play.
We hope to be a little bit more explicit.

***

It
is worthwhile to recall here that the CERES EBAF Ed2.8 all-sky
reflected solar radiation,
RSR(all) is 99.7 W/m2, and in the clear-sky part of the atmosphere the
reflected flux is RSR(clear) = 52.4 W/m2.

(Differences
between the successive versions of Ed2.6, Ed2.7 and Ed2.8 are within ±
0.5 W/m2.)

The
weighted contribuition of the clear and the cloudy part to this total
outgoing shortwave flux is:

In
possession of the clear-sky and all-sky data, the cloudy values can be
computed.

ASR(cloudy)
= [ ASR(all) – (1 – β)
× ASR(clear)] / β = 209
W/m2

SAA(cloudy)
= [ SAA(all) – (1 – β)
× SAA(clear)] / β
= 84 W/m2

SAS(cloudy)
= [ SAS(all) – (1 – β)
× SAS(clear)] / β = 125
W/m2.

The
cloudy surface energy balance equation is then:

E(SFC,
cloudy) = SAS(cloudy) + DLR(cloudy) =

=
2OLR(clear) – LWCRE / β
=

=
2OLR(cloudy) + LWCRE / β
=

= OLR(clear)
+ OLR(cloudy).

Evidently
the highly regulated clear-sky and the cloudy-sky solar absorptions and
reflections
require a well-organized and strictry controlled planetary-level
energetic cooperation between the two regions.

Isn't
the "buffering effect" beyond the "remarkably small interannual
variability", as mentioned by the albedo-paper, is based on the surface
energy budget constraint of the box model?

61.§.

It
seems also that even β, the single-layer IR-opaque equilibrium cloud
are fraction, is constrained at

β
= f0(all)
=
3/5.

For
our case, let us put the question in this
form:

Is
the energy budget of Earth highly constrained?

According
to the observed and published data, there is an arithmetic sequence of
fluxes,

and,
at the surface, the sum of energy flows in the balance equation are
restricted
to the energy flows at TOA:

So our answer, based on the observations, is yes,
the sum of energy flows at the lower boundary are
strictly constrained to the energy
flows at the upper boundary (TOA),
and seems to be independent of the
changing concentration of atmospheric IR-absorbing
trace gases.

On our
quasi-aquaplanet strict energetic
regulations control the radiative transfer
between
the boundaries and organize
the structure of energy flows into a well-ordered system.
The ‘building
blocks’ are multiples of the flux of longwave cloud effect,
and they create an atomic,
pattern-like, digital, quantized internal energy matrix structure;
we may call it under
different names, but the essence, as Galileo said, is in the numbers.
In our
case, in the observed, published CERES numbers.

*

62.§.

Evaporation,
clouds: stabilizing feedback?

It
seems
that evaporation and clouds play stabilizing role on the whole system:
latent
heat release is 3 all-sky units, controlling also the greenhouse factor
as 2LH
= G(all).

But it must be added that 2LH = G(all) is
only one of several internal relationships among the
'energy matrix' elements, but there are a lot of others, equally
important, and energetically
perhaps much more rigid relationships:

most importantly the E(SFC) = 2OLR + LWCRE,
which bounds the surface energies to that of at TOA.

Therefore do not think that they all are regulated by the
evaporation/cloud feedback.
They, all together, are strictly constrained by the
whole system of overall energetic restrictions.
These are digital ('quantum') states, 'grid positions' in the
chrystal structure sense.

Of course one may describe the vibrations of the atoms around their
lattice position in a chrystal,
or the stability of the electron orbit around the atomic
nucleus as controlled by 'feedbacks',
but we don't regard it is the most adequate conceptual framework.

***

This
is actually not a "climatic" problem, it is a physical
question:
how a drop of water (well, a big
drop of water) behaves in empty
space nearby a star.
It seems that its behavior is almost completely
predetermined (constrained, regulated)
by the incoming available energy.

63.§.

Clear-sky
pattern
as proposed by Miskolczi (2004, 2007, 2010, 2014)
We presented the clear-sky periodicity in this form:

This pattern was first recognized and the whole idea of a stationary
clear-sky
greenhouse structure,
based on line-by-line clear-sky computations, was
first presented by Miskolczi (2007).
The 2CTS(clear) = ULW relationship was published in Miskolczi and
Mlynczak (2004),
later it was referred to under the widely-criticized term of 'virial
rule'.

*The
validity of the STI(all) = LWCRE equation, and its possible role in the
system was noticed first in Miskolczi (2007): "the LW effect of the
cloud cover is equal to closing the IR atmospheric window".

*We have shown
above (39. § and 56.§) that their assumed LAA(clear) =
DLR(clear) equality
does not stand, therefore DLR(clear) does not have a grid position
here.
The clear-sky pattern is given this way
in Miskolczi (2014) The
greenhouse effect and the infrared radiative structure of the Earth's
atmosphere, Fig. 24. (Development in Earth Science, Volume
2.) :

Here FA
(absorbed solar radiation in the clear-sky part) is shown to be equal
to OLR(clear), and longwave atmospheric absorption, LAA, here AA,
is shown as
being equal to ED (DLR).
But these assumed equalities do not stand: according
to observations and computations, in reality
FA(clear)
– OLR(clear) = 287 – 266 = 21 W/m2,

Here K+
stands for the convective terms, K+ =
SH + LH. The role of K-
(downward sensible and latent heating?) is unclear in the energy
balance; the assumption of radiative equilibrium at the surface seems
questionable.

*

We think
that, contrary to some
problematic details of its presentation,
the clear-sky pattern and the corresponding original concept of a
steady state climate, as suggested by Miskolczi, is correct
and
supported by the data; the explanations and interpretations can be
clarified later.

*
A rather technical question may arise here: Are the annual global mean
clear-sky and
all-sky surface upward radiations equal? The answer is not necessarily
yes, but we recline here upon Kato et al.
(2013), Table 4, who shows an equality. In case of new data, this can
be refined.

*
DLR(clear) is measured by BSRN (Baseline Surface Radiation
Network,
Ohmura et al.) and given as

DLR(clear) = 319 (±9) W/m2 (see also Stephens et al 2012.),

its position in the clear-sky pattern is

DLR(clear) = 5 STI(clear) – LWCRE/2.

It has a position in the all-sky
structure as

TWELVE UNIT(all) = 12 LWCRE = 319.2 = 12 × 26.6 W/m2 = 319.2 W/m2,

showing the inter-connectedness of the clear and the all-sky values
through the globally determined and controlled relationship of

f(all) = β
= 0.6.

***

64.§.

Conclusion here:

Box 2: Discussion│Clear-sky

Incoming
solar radiation, according to CERES EBAF Ed2.7, is ISR = 339.8 W/m2,
reflected solar radiation in the clear-sky part of the atmosphere is
RSR(clear) = 52.6 W/m2.
This leaves for absorbed solar radiation in the clear-sky part of the
atmosphere,
ASR(clear) = 287.2 W/m2,
more than the clear-sky outgoing longwave radiation, OLR(clear) = 266
W/m2.

According to the same product, solar absorbed surface is SAS(clear) =
213.6 W/m2.
Therefore, solar absorbed by atmosphere is SAA(clear) = 73.6 W/m2.

and it can be seen that the clear-sky greenhouse effct equals to the
turbulent fluxes:

(SH + LH)(clear) = 133.8 W/m2 = G(clear) = OLR(clear) /2

again within Δ = 0.8 W/m2.

The cloudless
part of the atmosphere maintains
a strict, definite radiative transfer structure, with
'quantized' fluxes being equal toONE STI(clear) = 66.5 W/m2

TWO STI(clear) = G(clear) = 133.0 W/m2

THREE STI(clear) = CTS(clear) = 199.5 W/m2 = ULW/2

FOUR STI(clear) = OLR(clear) = 2 G(clear) = 266.0 W/m2

FIVE STI(clear) = LAA(clear) = 332.5 W/m2

SIX STI(clear) = ULW = 399.0 W/m2

and with a 'constrained' surface energy balance as

E(SFC, clear)
= 2OLR(clear).

The SIX units of clear-sky become NINE units of cloudy and FIFTEEN units of all-sky,
exactly
because the CLEAR and the CLOUDY areas are 6/15 and 9/15 of the TOTAL
surface, which means that the cloud area fraction is β
= 9/15 = 3/5.

***

65.§.

If
each element is quantized, and the energy budget is constrained,
then why is there global warming?

According
to the observed data, it is completely determined by the energy budget
at TOA.

As
always, Readers are asked to check these equalities themselves,
by substituting the data from the observations.

***

We
infer that present-day imbalance is not a long-term, ever-growing
process.

It
is a consequence of a temporary (natural or triggered) fluctuation
around the
energetically required, prescribed f0(all)
= 3/5 equilibrium.

Time-scale
of these fluctuations is not yet known.
Several processes might influence it, from decadal variations in the
cloud cover
to millennial changes in the deepwater global cycle,
each having their impact on surface temperature and ocean heat
content.

66.§.

LWCRE =
STI(all)

One of the most important elements of the
structure is the above relationship.

How could we understand this? What is the direction of causation?

Clouds
have two opposite effects on the system: a shielding effect in the SW,
and a blanketing effect in the LW. The former cools,
the latter warms
the surface, therefore the latter is called the greenhouse effct of
clouds.

LWCRE =>
STI(all)
Let
us approach the question from the energy minimum principle:
let us assume that the
system seeks its possible lowest energy state.

From this point of view,
the shielding effect is 'useful', the blanketing effect is 'harmful'.
Now the above equality can be read this way: The surface gets rid of
the superfluous cloud warming effect by an equivalent amount of energy
being lost in space through the open atmospheric window.

*
STI(all) => LWCRE

But the reading in the opposite direction is also possible.

If
the system wants to maximize its energy content (trying to behave like
a 'closed system'), then the spectral regions being transparent
(because of the molecular absorbing properties)
should be somehow made opaque.
The system solves the problem of closing the
open atmospheric window by the LW cloud effect;
by the help of LWCRE it
gains back the energy being lost in STI(all).

*

LWCRE <=> STI(all)

The
most probable solution is the mutual determination: the clear-sky
transparency depends on the water vapour content, as well as the cloud
amount. If STI(clear) is determined as OLR(clear)/4, and OLR(all) is
given by ASR, then LWCRE is connected to STI and beta, in both
directions:

The flow of the incoming solar radiative energy (ISR =
340.0 W/m2) through the climate system can be depicted as follows.

RSR = ISR × (1 – sin 45°) = 99.8 (± 0.2) W/m2

is reflected,

ASR = ISR × sin 45° = 240.2 (± 0.2) W/m2

is absorbed in the surface-atmosphere system.

***ASR
(9) = SAA (3) + SAS (6)

ASR, in the all-sky global average, is broken into
three equal parts.

One part is being absorbed by the atmosphere and clouds (SAA(all) =
79.8 W/m2):

the remaining two
is absorbed by the surface (SAS(all) = 160.4 W/m2; imbalance: 0.8 W/m2):

***

68. §

SAS(all) (6) =
G(all) (6)

The latter is being transformed into longwave radiation in
the surface,
serving the energy content of the all-sky greenhouse effect:

SAS(all) – IMB = G(all) = ULW – OLR(all) = 6 UNIT(all) = 159.6 W/m2

***
G(all) (6) = NSL(all) (2) + (SH + LH)(all) (4)

This amount of energy is again being devided into three equal parts.

One part of it serves as net surface longwave radiative cooling,

NSL(all) = ULW – DLR(all) = 2 UNIT(all) = 53.2 W/m2,

the remaining two parts serve as surface non-radiative cooling:

(SH + LH)(all) = 4 UNIT(all) = 106.4 W/m2

***

NSL(all) (2) = LWCRE
(1) + STI(all) (1)

NSL(all) itself is a sum of two equal quantities:

NSL(all) = LWCRE + STI(all)

***
LWQ (-7) = ULW (15) – OLR(all) (9) – DLR(all) (13)

The atmospheric all-sky greenhouse effect, G(all), augmented by one
unit of longwave cloud effect, LWCRE,
offers the energy content of upward atmospheric emission, called also
'cooling-to-space', CTS(atm),
and is equal to the total net atmospheric column cooling, LWQ:

At the surface, downward longwave radiation, added to surface absorbed
solar
radiation, DLR(all) + SAS(all), give the energies in the
surface
balance equation, and being balanced by the sum of radiative and non
radiative cooling of the surface:

the ratio of the clear- and the cloudy parts, (1
– β)/β
= 0.4/0.6 = f(clear) = 2/3 as
the clear-sky transfer function;

and the ratio of the clear-sky part to the total surface, (1
– β) = 0.4 = g(all) as the
all-sky greenhouse function

***

70.
§

Now
the all-sky greenhouse effect is connected to G(clear) as the clear-sky
outgoing longwave radiation is connected to OLR(all): through the value
of longwave cloud effect, LWCRE,

and the cloudy greenhouse effect to its clear-sky counterpart as the
clear OLR to the cloudy one:

These are our units of measure, or our

Augmented with the third unit, which is the measure under clear skies,

we have also the relationships between the three units.

***

71.
§

Now three of the basic elements of the energy flow system, ULW,
OLR(clear) and their difference, G(clear),
can be expressed with all of these units:

That is,

.

With the observed values,

***

All the other observed F fluxes can be written as

where

N is an integer between one and fifteen, and the units are given above.

With these, we get three periodic tables of fluxes in three different
units:

***

72. §

The observed all-sky (and where indicated, clear-sky) values are given
at the bottom of our poster:

The Δ difference
between the observed F values from their above-given F0
quantities
is much smaller than one standard daviation:***

73.
§

Let
us note: we have started the section with the observation that the
absorbed solar radiation in the all-sky system, ASR(all) = 240.2 W/m2,
is being devided into three
equal parts (one part is absorbed by the atmosphere, SAA(all) = 79.8
W/m2, and two parts are absorbed by the surface, SAS(all) = 160.4 W/m2).

Now
we should add: the solar radiation absorbed in the clear-sky part,
ASR(clear) = 287 W/m2 (data from CERES EBAF), is being devided into four
pieces: one is absorbed in the atmosphere (SAA(clear) = 72 W/m2, and
three is absorbed by the surface: SAS(clear) = 215 W/m2 (see e.g. Wild
2015b).

These latter quantity, added to the downward longwave radiation, take
up the total surface energy under clear skies:

E(SFC, clear) = SAS(clear) + DLR(clear) = 215 + 319 = 534
W/m2,

with a data-uncertainty of ± 5 W/m2.

This energy income is balanced by the radiative and non-radiative
energy release of the surface:

E(SFC, clear) = ULW + (SH + LH)(clear) = 399 + 133 W/m2

The two important points here are that the surface energy is conneted
to that of TOA as:

(a) E(SFC, clear) = 2 OLR(clear) ;

and the turbulent surface cooling is equal to the greenhouse effect:

(b) (SH + LH)(clear) = G(clear),

far within to the data observation error.

***

74.
§

Now the Cathedral of our Heavens above our heads seems to be carefully
designed and very well-constructed;
it is built from blocks or bricks of the following size:

The outgoing longwave radiation in the clear-sky part is being split
into FOUR equal parts:

The
size of these bricks is predestined by the size of the corresponding
OLR, and does not depend on the atmospheric chemistry. On the contrary,
the total effective atmospheric IR-absorber composition, including the
concentration and distribution of water vapor, seems to be regulated by
the design of the energy flows.

75. §

***

The
King among these radiations is atmospheric downward longwave emission
to the surface, DLR, called also "back-radiation"; once it was proposed
to
'another measure of the greenhouse effect' (Inamdar and Ramanathan
1997, On monitoring the atmospheric greenhouse effect from space.
Tellus 49B: 216-230).

A paper dealing solely with DLR says in its
Introduction:

"It
has been understood for some time that changes to the strength of the
greenhouse effect are fundamental to our understanding of the climate
of earth and how it can change (Arrenhius 1896; Callendar 1938; Kasting
1989). Increases in greenhouse gases like CO2 induce a warming of the
surface and lower atmosphere. The increase in water vapor that follows
a warming results in a further strengthening of the greenhouse effect
by increased emission of radiation from the atmosphere to the surface
that induces even more warming. This is the essence of the positive
water vapor feedback that occurs through the connections between
temperature, water vapor, and emission of infrared radiation (e.g.,
Held and Soden 2000)."

We think that while the paper presents correct observed data about the
clear-sky and all-sky DLR,
none of the above statements are supported by the data.

***

IPCC 2007 WGI AR4 Chapter 02 says:

"Philipona
et al. (2004) found an increase in the measured longwave downward
radiation at the surface over the period from 1995 to 2002 at eight
stations over the central Alps. A significant increase in the clear-sky
longwave downward flux was found to be due to an enhanced greenhouse
effect after combining the measurements with model calculations to
estimate the contribution from increases in temperature and humidity."

We think that temporal
and local
changes in the clear-sky downward flux cannot be attributed to an
enhanced greenhouse effect. Or, if its measured value still increases,
it is because it was below
of its equilibrium position.

The stability to the strength
of the global
greenhouse effect is fundamental to the climate of earth,
and
both the clear-sky and the all-sky downward atmospheric emission sit
very sharply in their given grid
position:

The above paper from Stephens et al. says DLR(all) is between 344 and
350 W/m2.
Stephens et al. (2012) give DLR = 345.6 W/m2,
its pattern position in our diagram is 345.8 W/m2.
We show DLR(all) as a sum of three components:

That
is the quantity which is expected (by the prevailing theory) to undergo
the largest increase of all radiative fluxes over this century:Wild M (2011) BSRN:
Science and Operations UpdateAOPC-XVI, WMO,
Geneva, Feb. 8 2011.

As said, its observed value today, as proposed by Stephens et al.
(2012), is 345.6 W/m2:
it occupies its grid position within 0.2 W/m2.

It is sitting sharply in its prescribed all-sky global mean position of
13 LWCRE.

That's why we think that the above-proposed increase cannot (and will
not) happen.
(For the source of the asymmetry, see more details in the
"Cooling-to-space approximation" section above, 56. §)

76.
§

***

The Queen of all these energies, the greenhouse effect itself, being
defined as the difference of surface emission
and outgoing radiation, G = ULW – OLR, can
also be understood as follows:

— In the clear-sky part, it is equal to the non-radiative surface
energy release:

G(clear) = (SH + LH)(clear) = 133.0 W/m2,

and equals also to TWO clear-sky units (2 × 66.5 W/m2);

— In the cloudy
part, it is equal to the double
of the non-radiative energy flows:

G(cloudy) = 2 (SH + LH)(cloudy) = 2 × 88.66 W/m2 = 177.33 W/m2,

being equal to FOUR cloudy units (4 × 44.33 W/m2)

(in the cavity of the surface-cloud box, it seems something like
thermals up plus thermals down);

— and in the all-sky mean, it equals to the
sum of the surface non-radiative and net radiative cooling:

G(all) = (SH + LH)(all) + NSL(all) = 106.4 + 53.2 = 159.6 W/m2,

being equal to SIX all-sky units (6 × 26.6 W/m2).

Note that the surface, in the all-sky mean, cools non-radiatively twice
as much as radiatively:

=+

The longwave energy content of G(all), gained from the solar
absorption by the surface, SAS(all), in
the all-sky mean is completely counter-balanced by the surface
non-radiative plus net radiative cooling.

The contribution of the cloudless part to the all-sky mean is 0.4 ×
133.0 = 53.2 W/m2, which is TWO all-sky units;

the contribution of
the cloudy part to the all-sky mean is 0.6 × 177.33 = 106.4 W/m2, which
is FOUR all-sky units;

so
the G(all) = SIX all-sky mean is again being devided into three equal parts:
one
is coming from the clear atmosphere, and two from the cloudy.

77.
§

That's
why we think that the increase of the greenhouse effect, as predicted
by the prevailing theory (cited in our Introduction from Wild 2015a),
will not happen:

That's how, we think, the absorbed solar radiation is partitioned
into the found units,
creating the
wonderfully designed composition we experience.

***

79.
§

Our
Sun seems to be
quite happy with these new results.

80. §

Theory

It
is evident that in the present state of the work, we cannot give a
complete conceptual descripition, a new hypothesis or theory on how our
climate system might work that mainatins the given patterns,
periodicities and structure. So our comments will be necessarily
inconclusive, and we just repeat here what we have said in the
Introduction.

In the real case of the
partially SW-transparent, partially LW-opaque and partially
cloud-covered Earth,
the surface energy is still
uniquely determined by the energy flows at TOA, in the form of

E(SFC, clear) = 2OLR(clear) ,

82. §

E(SFC, all) = 2OLR(clear) –
STI(all) = 2OLR(all) + LWCRE.

and

E(SFC, cloudy) = OLR(cloudy) + OLR(clear).

The question appears, how the system solves the problem of becoming
LW-opaque,
that is, of "closing the atmospheric window".

*

Costa and Shine (2012) note that about
"one-tenth of the OLR originates directly from the surface".

This also means that only about one-fifteenth of the surface emission
reaches directly to space.
That is, our atmosphere is 'almost-closed'.

Kiehl and Trenberth (1997) when calculating LWCRE (their Fig. 2) note
that
"the largest effect of clouds on the outgoing longwave flux is in the
atmospheric
window (8–12 micron)"

Their values were STI(all) = 40 W/m2 and LWCRE = 30 W/m2.

Now we have seen that with STI(clear) = 66.5 W/m2 of Costa and Shine
and β = 0.6 of CERES,

it is true that
STI(all) = (1 – β) ×
STI(clear) = LWCRE.
Now the answer may lay in the

83.
§

STI(all) = LWCRE

equality,

which
says that

the surface transmitted LW energy being lost in the open
atmospheric window
is given back to the surface by the equivalent
amount of energy in the cloud greenhouse effect.

In
a "leaky" atmosphere the energy content of STI(all) is "lost in space"
from a surface viewpont; but in a "closed by clouds" atmosphere the
energy content of STI(all) is gained back by the greenhouse effect of
clouds.

In this sense,
the energetic role of the partial cloud cover in the LW is to close the
atmospheric window —
that is, to make the system non-transparent in the
infrared.

***

84. §

In another frasing:

As the atmosphere is not saturated for the LW-absorption
(becouse
of the molecular absorption properties, there is a transparent region
in the H2O, as well as in the CO2-spectrum), the LW-blanketing effect
of the clouds is called into the sceen to help to keep the energy "in".

This kind of "closed" character is reflected in the simple (and easily
controllable) relationships of

2 G(clear) = OLR(clear)

saying
that the upwelling and downwelling LW energies in the clear-sky
greenhouse effect utilize the entire amount of LW energy in the
outgoing radiation;

2 CTS(clear) = ULW

saying that the atmospheric upward emission in the clear-sky part is
double of the surface energy;
this equality maps the 2OLR = ULW glass-shell relationship, as
OLR(clear) = CTS(clear) + STI(clear);

2 CTS(atm) = LAA(all)

this
one says that in the all-sky case, atmospheric LW absorption, which is
ULW less STI(all), is double of the all-sky atmospheric upward emission:

This "wave in a box" character seems to appear in the integer multiples
of the internal fluxes:

LWCRE = ONE STI(all)

NSL(all) = TWO LWCRE, etc.

and in all the presented internal integer ratios and proportions.

As an analogy, in lack of a better explanation,
should we call the propagating energy in the "box" a "wave",
and N in the F = N × UNIT equation "wave number"?

***

The
conclusive statement here would be evidently to show how this result
can be deduced from some first principles — say, from the
principle of least action.

Part of the deduction may go like this:

One
of the most universal physical laws is the
principle
of energy minimum: a ball at the bottom of a potential hole, or the
cooling of
a hot stove in a cold room. The hot surface of the Earth cools two
different ways: by turbulent (latent + sensible) heat release, and by
radiative
cooling. The most efficient (maximized) latent cooling maximizes the
atmospheric water vapor content (greenhouse gas), leading to the
narrowest
(tightest) atmospheric window (lowest IR transparency). The most
efficient
radiative cooling of the surface into the space requires the widest
atmospheric
window (highest IR transparency). On our aqua-planet, there is an
evident equilibrium between the two opposite constraints: the ratio of
the
turbulent/radiative cooling is predetermined by physical constants:
sea-flux/Planck-flux must be a given, fixed value.

***

85. §.

Closing
remarks

"It
is unequivocal
that anthropogenic increases in the well-mixed greenhouse gases
(WMGHGs) have substantially enhanced the greenhouse effect, and the
resulting forcing continues to increase."
– says the very first sentence of the Executive Summary of IPCC 2013
Working Group I AR5, Chapter 8.

[In:
Climate Change 2013: The Physical Science Basis. Contribution of
Working Group I to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change. Cambridge University Press]

We hope we have shown here that it is NOT
unequivocal that
anthropogenic increases in WMGHG's have at all enhanced the
greenhouse effect.

We didn't want to introduce a counter-hypothesis here; we did
not insist or assert anything speculative.

We just state that, according to the observed data, the greenhouse
effect sits very stably in its
1/3 and 2/5 clear-sky and all-sky pre-fixed 'grid' value.

Our purpose was to show these 'observations' about the
characteristics
of the published energy budget data, and to share our contemplations
about them to trigger a discussion.

86.
§.

Box 3:
Discussion│Conclusion

We have written this large website on the climate system, and have
never even mentioned CO2.

We have no need of that hypothesis.

This is a closed system,
the LW energy being lost in the atmospheric window
is gained back by the LW cloud effect.

The surface energy budget and the F fluxes are
unequivocally determined by the TOA fluxes:

E(SFC, clear) = 2OLR(clear)

E(SFC, all) = 2OLR(all) + LWCRE,

F(all) = I × LWCRE,

LWCRE = OLR(all) / 9 = OLR(clear) / 10.
CO2 is not the “control knob” of the energy flow system,
neither of the greenhouse effect, nor of the surface and atmospheric
radiations.

These values are energetically
pre-determined,
sitting very sharply in
their prescribed 'quantized' position.

Beyond the flux arithmetic patterns,
there is a tight, controlled connection
between the clear-sky and the all-sky part, through the constraints of:

an albedo with the observed value of

albedo = 1 – sin 45° = 1 – √2/2
= 0.293

and the cloud area fraction with the
observed value and relationship of

beta = f0(all)
= 3/5.

On the planetary level, the whole
system seems to have a symmetrical, highly regulated chrystal-ball
structure, completely
constrained to the incoming solar radiation.

87. §

Conclusions

HARMONIA
PLANETARIS

Stations of a
cooperation
Pictures of an exhibition

Deduction of the basic characteristic of Earth's energy budget in 4
steps:

I.
Schematic model
of a planet closed into a greenhouse
(SW-transparent, LW-opaque,
non-turbulent):

II.
Schematic model
of the clear-sky part of the Earth's atmosphere
(semi-transparent in SW and LW, turbulent):

In the cloud-free part
of the atmosphere the reflected solar radiation is less,
the absorbed solar radiation is more than in the global average all-sky
case.

SAA + SAS =
ASR > OLR

Further, DLR is higher
than OLR,
ULW is lower than 2OLR

DLR >
OLR

ULW < 2OLR

There is turbulent heat
transfer from the surface into the atmosphere, SH + LH > 0.

And still, according to
CERES data:

OLR(clear) = 266 W/m2

ASR(clear) = 287 W/m2

SAA(clear) = 74 W/m2

SAS(clear) = 213 W/m2

DLR(clear) = 319 W/m2

E(SFC, clear)
= SAS + DLR = ULW + SH + LH = 2OLR(clear)

*

III.
Schematic model
of the cloudy part of the Earth's atmosphere
(semi-transparent in SW, opaque in LW, turbulent):

In the cloudy part of
the atmosphere the reflected solar radiation is more,
the absorbed solar radiation is less than in the global average all-sky
case.

SAA + SAS =
ASR < OLR,

There is no longwave
surface transmission through the clouds:

STI(cloudy) = 0.

DLR >
OLR, ULW < 2OLR,
SH + LH > 0.

And still ...

E(SFC, cloudy)
= SAS + DLR = ULW + SH + LH = OLR(cloudy) +
OLR(clear)

*

IV.
Schematic model
of the all-sky atmosphere of
Earth
(semi-transparent in SW and LW, turbulent):

In
the all-sky mean, Earth maintains a delicate equilibrium on the
planetary level
between two very different areas: the cloudless and the cloudy parts of
the
atmosphere.
The cloudy part blocks, the cloudless part allows a surface
transmission
that is equilibrated to the longwave cloud radiative
effect.

The cloud area fraction
is also part of the cooperation which
finally leads to a
constrained surface energy budget and a
definite energy flow structure:

As a result of the
'closed-into-a-glass-shell-greenhouse' model,
the energy flows show a discrete, integer-multiple characteristic.

We presented the observed
values
of the F flux terms in Earth’s global energy budget as

F = F0 + ΔF, where F0 = N
× U; N is an integer, U is a
unit flux and ΔF is a deviation.

Based on the published data we have shown that:

with the flux unit U =
LWCRE, the elements fit into an all-sky pattern;
with U = LWCRE/ β into a
cloudy pattern, and
with U = LWCRE/(1
– β) =
STI(clear) into a clear-sky pattern.

The ΔF deviations
of the observed F values from their F0
pattern positions are smaller
(typically
within ±2 W/m2) than ±1σ range (typically ± 4W/m2) of data
uncertainty.

***

According to the data, in the global average,
the sum of the energy flows
at the surface seems to be unambiguously determined
by the energy flows at
TOA,
within an imbalance, separately for the clear, cloudy and the all-sky
case:

E(SFC, clear) = 2OLR(clear)

E(SFC, cloudy) = OLR(clear) + OLR(cloudy)

E(SFC, all) = OLR(clear) + OLR(all) .

***

From the 'leaky closed model' we can deduce the actual interconnections.

In the closed case, both the transfer and the greenhouse
function have a value of 0.5.

On Earth,
where STI(all) / OLR(clear) = 1/10, i.e.,

one-tenth of the clear-sky emission is a 'lost-in-space' surface
radiation through the all-sky atmospheric window,

From here, with the all-sky planetary emissivity of OLR(all) / ULW =
9/15 = 0.6
we have for the clear-sky value of the transfer and greenhouse
functions:

f(clear) = 9/15 + 1/15 = 2/3,

g(clear) = 6/15
– 1/15 = 1/3.
***

The longwave-regulated
β0
= f0(all)
=
3/5 energetic requirement
then maintains a cooperation
between the clouds and the surface, leading to a constrained

ASR / ISR = 240.4 /340.0
= sin 45° = √2/2

shortwave absorption ratio and a

symmetric planetary albedo of

α0
= 1 – sin 45° = 1
– √2/2 = 0.293.
.

89.§.

Consequences

If this pattern is not purely
coincidental but represents
reality,
then the whole-number units maintain the given vulgar fractions, ratios
and relationships,
and prevent the
global state from continuous shifts and smooth internal
reorganization.

As long as the all-sky flux values are multiples of LWCRE = OLR(all)/9,
it can be
inferred that

[ The term "enhanced, elevated, increased
greenhouse effect" is used
as in the IPCC (2013) WGI AR5 Chapter 02 and Chapter 08;
and would mean that ULW grows without increasing ASR or OLR. ]

OLR(all) is made up from 9 blocks or bricks or quanta, OLR = 9
LWCRE,
ULW is made up from 15 blocks or bricks or quanta: ULW = 15 LWCRE.

They can move only together; the equilibrium all-sky transfer
function is

f(all) = OLR/ULW = 9/15 = 3/5,

therefore the equilibrium all-sky greenhouse factor is

g = 1
– f =
(ULW –
OLR)/ ULW = G(all)/ULW = 2/5 = 0.4,

and no smooth tendency or shift is possible.

Only vibrations, natural or externally triggered,
annual or decadal or centennial or millennial or longer
variability is allowed around the
'grid' (F0) value.

*

If the structure described here is true
– and it seems to us that all
the fluxes occupy their F0 position
precisely –,

than ULW, and G, and g
cannot increase without an increase in ASR (or OLR).

*

That's why we say that the equilibrium greenhouse
sensitivity is zero for increasing CO2.

Note:

The latter does not
mean that CO2, H2O do not
have IR emission/absorption.
It means only that, according to the published CERES
data,
all the fluxes are sitting in their pre-determined position.
Therefore, the whole atmospheric temperature and IR
absorption/emission structure
(including the water vapor amount, greenhouse effect
magnitude and cloud formation)
is created, organized, prescribed and maintained by
the
albedo - cloud area fraction - SW absorption - LW emission
(and evaporation, precipitation, atmospheric IR transparency,
window value etc.)
structure.

-
"Holding the increase in
the global average temperature to well below 2
°C above pre-industrial levels",
as the Paris Climate Agreement says, assumes an invalid
direct connection
between CO2 and global temperatures.

We may infer further from here that:

The
model-predicted gradual 30 W/m2 increase in the flux of DLR to the
end of this century, as a function of changing surface air temperature
forced by a 1% per year increase in CO2, as shown in
the
Supplementary Information to the Stephens et al. (2012) Nature
Geoscience paper, is not possible:

Stephens et al.
2012 NGEO1580 Suppl Inf Figure S2 (c)

The main
consequence of our results can be given in the verifiable form
of a forecast:

if
the structure we have presented in our paper and in this website is
true;if
the flux values continue to occupy their grid position as
whole-number multiples of LWCRE;if
LWCRE remains a brick being equal to one-ninth of OLR(all);if
DLR remains to be built up from 13 bricks of LWCRE

then
the model-predicted smooth or gradual increase in DLR as a result
of increasing CO2,
as shown in a Wild 2011 WMO presentation

Some
of the fundamental observable flux parameters are accurately measured
to accept their values, most notably the basic LW boundary fluxes: ULW,
OLR and DLR; their deviation from their grid position is within 1
W/m2.

SW fluxes are slightly less certain; and the turbulent fluxes, mainly
sensible heat, are the most uncertain.

The
computed fluxes depend on the atmospheric data base and the computer
code; the most essential parameter, clear-sky window flux can be
regarded as 66 ± 2 W/m2.

The largest source of uncertainty is the value of cloud area fraction.

The
CERES project from March 2000 to March 2016 has 62% cloudiness for the
first decade, then an average of 60.5% for the last seven or so years.

We
regard the single-layer IR-opaque effective cloud amound (area
fraction) as beta = 0.60, therefore our STI(all) = 66 × (1 – 0.6) =
26.4 W/m2 is higher than the one based on the ISCCP data.
Further
observational and modelling efforts are needed to have an objectively
established magnitude for this fundamental climate parameter.

In
the all-sky mean, Earth
has higherDLR andlowerULW
than in the closed shell model,

and
the difference in both cases is the turbulent flux:

DLR(all)
= OLR(all) + (SH + LH)(all)

and

ULW
= E(SFC, all) – (SH + LH)(all).

II.

We showed that in
the above-said LWCRE-modulated 'closed box' model,
the energy flows follow a discrete pattern:
the
global average
clear-sky, cloudy-sky and
all-sky energy flows
can be written as integer multiples of a certain 'energy quantum',
which is the flux
element of LWCRE/(1
– β), LWCRE/β,
and LWCRE:

According to the published data, the ΔF deviation of the observed F
values from the proposed F0 equilibrium
positions is typically less than ±2 W/m2, much less than
the known observation error. This means that all F values are in the
neighborhood of their F0 position within one
standard deviation. This suggests that all fluxes in our
system occupy their 'grid'
position very closely, being an integer multiple of the atmospheric
flux energy quantum, with only small fluctuations around it, without
a detectable systematic deviation.

III.
The
amount of clouds seems also highly regulated, and the IR-opaque
single-layer cloud area fraction
equals to the
all-sky transfer function (planetary
emissivity),
each having a preferred equilibrium value of 9/15:

β0
= f0(all)
= ep
= 0.6.

Accepting the components of ep = OLR(all) / ULW
as

OLR(all) = 239.6 W/m2 =
9 LWCRE = 9 × 26.6 W/m2
+ 0.2 W/m2

and

ULW = 399.0 W/m2 = 15
LWCRE = 15 × 26.6 W/m2 +
0.0 W/m2,

the planetary emissivity is very close to, but eventually slightly
above of its required value

The same is true for the cloud area fraction: it is also slighly above
its energetically prescribed value.

Both of them is expected to decrease, leading to some further warming.

In other words:

Having these OLR and ULW values, the greenhouse effect today is 0.2
W/m2 lower than it ought to be.

If we believe in these data, we do not have an enhanced greenhouse
effect today;
we have a decreased
greenhouse effect.

IV.
We have also recognized an equilibrium position for the Earth's albedo
at

α0
= 1 – sin 45° = 1
– √2/2 = 0.293.

*

If
these four types of constraints prove to be long-standing and valid,
then they might
have a common physical origin, and together represent an
energetically prescribed,
constrained and quantized equilibrium (steady) state of our
climate system.

Recent
warming then might not be greenhouse warming but only natural or
triggered oscillation (vibration) on
historical time scale around
the preferred equilibrium state.

***

94. §

Let us imagine, just for a moment, an idealized hypothetical world,
where The New York Times
is interested in climate science, instead of climate ideology.

Let us assume that we are asked to give their online edition
a Breaking News Headline, a figure, and some answers.

Q: Are these ratios and relationships always valid?
A: What we can firmly state is that now
they are valid. We can read them out from the published data.
But we
cannot see any reason why they shouldn't be valid at any time. The
numbers are integers, defined by the geometry, and not approximated
real numbers.

Q: Are they depending on the atmospheric CO2
content?
A: No; they are depending only on the structure; and this is a rigid
structure,
where no internal deformations but only 'vibrations' are possible.
The whole construction is very stable and depends only on the available
energy.

Q: Why?
A: Earth behaves as a closed system (like a planet in a real
greenhouse).
Its open atmospheric window (small infrared transparency) is closed by
the greenhouse effect of clouds, and within this closed geometry the
energy budget is limited.

Q: Why?
A: Energetic limits at the upper boundary specify the behavior of the
whole system,
including the energy budget at the lower boundary.

Q: Why?
A: Physical principles like the energy minimum or the principle of
least action might work in the background.

Q: Does this mean that there is no climate change?
A: If under 'climate change' you mean CO2-induced
enhanced greenhouse effect, that
kind of climate change does not exist.

Q: What kind of climate change exists, then?
A: First, the observed planetary emissivity is recently
slightly above its
prescribed value of 3/5;
it must decrease.
Second, we are talking about annual global means. One and the same
annual global mean can be implemented through several different
regional, vertical and seasonal distributions;
changing CO2-concentrations
might change these distributions.
Third,
there are always fluctuations, natural or triggered oscillations
around the equilibrium position, with unknown size and time-scale.
Fourth,
the regional distribution of the absorbed solar radiation might be
different under different cloud regimes – even if the global mean
is the same.
Fifth, there are evident quasi-periodic changes in the astronomical
parameters and in the insolation.

Q: Should we reduce our CO2-emissions?
A:
Our results show that the equilibrium greenhouse sensitivity is zero. As
all the basic parameters are surprisingly close to their theoretically
predetermined position, the
transient
greenhouse sensitivity cannot be high either. The equilibrium climate
sensitivity (which is influenced by indirect, secondary factors
such as change in cloud type and distribution, leading to changing geographic
insolation
and local albedo) is unknown. The fact is that the greenhouse factor is
currently slightly less
than its energetically required long-term equilibrium g = 2/5.

*
Let us add: New paper published in NATURE Scientific Reports finds
A Hiatus of the Greenhouse Effect.
Their values are 399, 345, 240 and 158 W/m2 for surface upward longwave
radiation,
downward longwave radiation, outgoing longwave radiation, and the G
greenhouse effect.

This means that both DLR and G are below
their steady-state position required by the absorbed solar
energy.

We do not have an enhanced
greenhouse effect;
in these decades we experience a reduced greenhouse
effect,
slowly fluctuating around its prescribed stable value.

*The
annual global mean energy budget of the Earth, as a whole,
is constrained and quantized,
including clouds and albedo,
but regional and seasonal redistrubition is possible.
A planned,
technology-driven long-term emissions reduction strategy
wouldn't be
unwise to mitigate the reorganization;
but the logic of preventing a 2 °C greenhouse warming is
fundamentally faulty.

95. §

***

Okay then, but where is the ideology? What is the new religion?

Here is one; not the best, not the last.

We are travelling in a well-constructed spacecraft, where almost
everything is designed;
chance
and contingency play only little role. The shortwave reflection and
absorption, the cloudiness, the longwave whole-number flux
distribution, the
surface and atmospheric energy balance — all of these things are
planned, prescribed, predetermined by physical laws and operated by a
well-functioning machinery in an implicit order.

When albedo regulation is explained, a current paper
calls 'Gaia' into the scene
(Stephens
et al. 2015: The albedo of Earth).

(Gaia. Design:
Szekely Berta, 1987)

Which almighty God should we refer to, when the
stability of the
entire shortwave - longwave - cloudy - planetary budget is to be
understood?

(Oops, we have almost repeated Kepler's
error here: we feel the temptation to expand the
found aritmetic pattern into a metaphysical
world
view! Be careful...)

*

Yes,
the above-said 'creationist', 'constructivist' explanation is probably
incorrect,
or at least incomplete — but that is the nature of the human mind:
wants to look behind the curtain to find the rule and law for
the observed evidence.

The End.

***

If the reader disagrees
with us, it's fine. Let us refer to
the French moralist Joseph Joubert:

1.
We were told our tables were hideosly complex. If readers were able to
understand such pages half thousand years ago we hope they
will be
able to get to grips with ours as well today.2.
"To search for something – though it be mushrooms – or some pattern –
is impossible, unless you look and try." Dmitri Mendeleev, Fundamentals
of Chemistry, 1903.

3.
In a sense, we are Kepler-followers: "a mind to whom all
ultimate reality, the essence of religion, of truth and beauty, was
contained in the language of numbers." Arthur Koestler: The
Sleepwalkers. Macmillan, 1959.4.
An intuitively accurate, but wrong model is Niels Bohr's model
of
the atom, where electrons are restricted to special energies with
integer multiples of a unit energy.

6.
Actually, we have the inverse
problem of climate change.John von Neumann,
his wife Klari, and their dog Inverse

"Weather prediction is an initial value problem, climate
prediction is a boundary condition problem" - he used to say. Applying
the correct annual global mean
boundary conditions – flux, cloud, albedo and energy budget stability
constraints – on a 2 × CO2 atmosphere, GCMs might have the chance to
provide us with some clue on the regional and seasonal
distribution of the
possible changes.7.
Did you know? Aristotle in his Meteorology lays down the basics of
ocean Salinity and Flow:

"Let
us explain the nature of the sea and the reason why such a large
mass of water is salt and the way in which it originally came
to be.

The
old writers who invented theogonies say that the sea has
springs, for they want earth and sea to have foundations and
roots
of their own. Presumably they thought that this view was
grander
and
more impressive as implying that our earth was an important
part of the universe. For they believed that the whole
world had been built up round our earth and for its sake, and
that the earth was the most important and primary part of it.
Others, wiser in human knowledge, give an account of its origin.
At first, they say, the earth was surrounded by moisture. Then
the
sun
began to dry it up, part of it evaporated and is the cause
of winds and the turnings back of the sun and the moon,
while the remainder forms the sea. So the sea is being dried up
and is growing less, and will end by being some day entirely
dried up. Others say that the sea is a kind of sweat exuded
by the
earth when the sun heats it, and that this explains its saltness:
for all sweat is salt. Others say that the saltness is due to
the
earth. Just as water strained through ashes becomes salt,
so the sea owes its saltness to the admixture of earth with
similar properties." (...)

"The
whole of the Mediterranean does actually flow. The directionof
this flow is determined by the depth of the basins and by the
number of rivers. Maeotis flows into Pontus and Pontus into
the
Aegean.
After that the flow of the remaining seas is not so easy to
observe. The current of Maeotis and Pontus is due to the
number of rivers (more rivers flow into the Euxine and
Maeotis than into the whole Mediterranean with its much
larger basin), and to their own shallowness. For we find the sea
getting deeper and deeper. Pontus is deeper than Maeotis, the
Aegean than
Pontus, the Sicilian sea than the Aegean; the Sardinian and
Tyrrhenic being the deepest of all. (Outside the pillars of
Heracles the sea is shallow owing to the mud, but calm, for
it lies in a hollow.) We see, then, that just as single
rivers flow from mountains, so it is with the earth as a
whole: the greatest volume of water flows from the higher
regions
in the
north. Their alluvium makes the northern seas shallow,
while the outer seas are deeper. Some further evidence of
the height of the northern regions of the earth is afforded
by the view of many of the ancient meteorologists. They
believed that the sun did not pass below the earth, but round
its northern part, and that it was the height of this which
obscured
the sun and caused night."

(Which translation would you prefer?)8. A
map from 1935 shows the Mediterranean-Atlantic salt tongue this way:The slightest change in
the Thermohalin Circulation might lead to change in the amount of
upwelling coldwater from the abyss during the La Nina events, causing
unpredictable variation in sea surface temperatures.

9.
The best-known example for internal variability is the
Broecker-conveyor: